From 43f88eb9fd7c2f143069ec3019e25e4bd9ddf023 Mon Sep 17 00:00:00 2001
From: "Sebastian G. Mutz" <sebastian@mutz.science>
Date: Thu, 8 May 2025 11:51:50 +0200
Subject: [PATCH 1/7] modified parameterisation for stats exp dist. procedures

---
 .../example_exponential_cdf.f90               |  58 ++++---
 .../example_exponential_pdf.f90               |  55 ++++---
 .../example_exponential_rvs.f90               |  26 ++-
 ...stdlib_stats_distribution_exponential.fypp |  70 ++++----
 test/stats/test_distribution_exponential.fypp | 154 +++++++++---------
 5 files changed, 193 insertions(+), 170 deletions(-)

diff --git a/example/stats_distribution_exponential/example_exponential_cdf.f90 b/example/stats_distribution_exponential/example_exponential_cdf.f90
index 9f108a686..f319662c4 100644
--- a/example/stats_distribution_exponential/example_exponential_cdf.f90
+++ b/example/stats_distribution_exponential/example_exponential_cdf.f90
@@ -4,60 +4,72 @@ program example_exponential_cdf
                                                    rexp => rvs_exp
 
   implicit none
-  real, dimension(2, 3, 4) :: x, lambda
+  real, dimension(2, 3, 4) :: x, loc, scale
   real :: xsum
-  complex :: scale
+  complex :: cloc, cscale
   integer :: seed_put, seed_get, i
 
   seed_put = 1234567
   call random_seed(seed_put, seed_get)
 
-  ! standard exponential cumulative distribution at x=1.0
-  print *, exp_cdf(1.0, 1.0)
+  ! standard exponential cumulative distribution at x=1.0 with loc=0.0, scale=1.0
+  print *, exp_cdf(1.0, 0.0, 1.0)
   ! 0.632120550
 
-  ! cumulative distribution at x=2.0 with lambda=2
-  print *, exp_cdf(2.0, 2.0)
+  ! cumulative distribution at x=2.0 with loc=0.0 and scale=0.5 (equivalent of lambda=2)
+  print *, exp_cdf(2.0, 0.0, 0.5)
   ! 0.981684387
 
-  ! cumulative distribution at x=2.0 with lambda=-1.0 (out of range)
-  print *, exp_cdf(2.0, -1.0) 
+  ! cumulative distribution at x=2.5 with loc=0.5 and scale=0.5 (equivalent of lambda=2)
+  print *, exp_cdf(2.5, 0.5, 0.5)
+  ! 0.981684387
+
+  ! cumulative distribution at x=2.0 with loc=0.0 and scale=-1.0 (out of range)
+  print *, exp_cdf(2.0, 0.0, -1.0)
   ! NaN
 
+  ! cumulative distribution at x=0.5 with loc=1.0 and scale=1.0, putting x below the minimum
+  print *, exp_cdf(0.5, 1.0, 1.0)
+  ! 0.00000000
+
    ! standard exponential random variates array
-  x = reshape(rexp(0.5, 24), [2, 3, 4])
+  x = reshape(rexp(0.0, 2.0, 24), [2, 3, 4])
 
   ! a rank-3 exponential cumulative distribution
-  lambda(:, :, :) = 0.5
-  print *, exp_cdf(x, lambda)
+  loc(:, :, :)   = 0.0
+  scale(:, :, :) = 2.0
+  print *, exp_cdf(x, loc, scale)
   ! 0.301409245  0.335173965  5.94930053E-02  0.113003314
   ! 0.365694344  0.583515942  0.113774836     0.838585377
   ! 0.509324908  0.127967060  0.857194781     0.893231630
   ! 0.355383813  0.470882893  0.574203610     0.799321830
   ! 0.546216846  0.111995399  0.801794767     0.922525287
-  ! 0.937719882  0.301136374  3.44503522E-02  0.134661376 
+  ! 0.937719882  0.301136374  3.44503522E-02  0.134661376
+
 
-  ! cumulative distribution array where lambda<=0.0 for certain elements 
-  print *, exp_cdf([1.0, 1.0, 1.0], [1.0, 0.0, -1.0])
+  ! cumulative distribution array where scale<=0.0 for certain elements
+  print *, exp_cdf([1.0, 1.0, 1.0], [0.0, 0.0, 0.0], [1.0, 0.0, -1.0])
   ! 0.632120550  NaN NaN
 
-  ! `cdf_exp` is pure and, thus, can be called concurrently 
+  ! `cdf_exp` is pure and, thus, can be called concurrently
   xsum = 0.0
   do concurrent (i=1:size(x,3))
-    xsum = xsum + sum(exp_cdf(x(:,:,i), lambda(:,:,i)))
+    xsum = xsum + sum(exp_cdf(x(:,:,i), loc(:,:,i), scale(:,:,i)))
   end do
   print *, xsum
   ! 11.0886612
 
-  ! complex exponential cumulative distribution at (0.5,0.5) with real part of
-  ! lambda=0.5 and imaginary part of lambda=1.0
-  scale = (0.5, 1.0)
-  print *, exp_cdf((0.5, 0.5), scale)
+  ! complex exponential cumulative distribution at (0.5, 0.0, 2) with real part of
+  ! scale=2 and imaginary part of scale=1.0
+  cloc   = (0.0, 0.0)
+  cscale = (2, 1.0)
+  print *, exp_cdf((0.5, 0.5), cloc, cscale)
   ! 8.70351046E-02
 
-  ! As above, but with lambda%im < 0 
-  scale = (1.0, -2.0)
-  print *, exp_cdf((1.5, 1.0), scale)
+  ! As above, but with scale%im < 0
+  cloc   = (0.0, 0.0)
+  cscale = (1.0, -2.0)
+  print *, exp_cdf((1.5, 1.0), cloc, cscale)
   ! NaN
 
 end program example_exponential_cdf
diff --git a/example/stats_distribution_exponential/example_exponential_pdf.f90 b/example/stats_distribution_exponential/example_exponential_pdf.f90
index 77c534f7f..3f4ef6c2e 100644
--- a/example/stats_distribution_exponential/example_exponential_pdf.f90
+++ b/example/stats_distribution_exponential/example_exponential_pdf.f90
@@ -4,59 +4,66 @@ program example_exponential_pdf
                                                     rexp => rvs_exp
 
   implicit none
-  real, dimension(2, 3, 4) :: x, lambda
+  real, dimension(2, 3, 4) :: x, loc, scale
   real :: xsum
-  complex :: scale
+  complex :: cloc, cscale
   integer :: seed_put, seed_get, i
 
   seed_put = 1234567
   call random_seed(seed_put, seed_get)
 
-  ! probability density at x=1.0 in standard exponential
-  print *, exp_pdf(1.0, 1.0)
+  ! probability density at x=1.0 with loc=0 and in standard exponential
+  print *, exp_pdf(1.0, 0.0, 1.0)
   ! 0.367879450
 
-  ! probability density at x=2.0 with lambda=2.0
-  print *, exp_pdf(2.0, 2.0) 
+  ! probability density at x=2.0 with loc=0.0 and scale=0.5 (lambda=2.0)
+  print *, exp_pdf(2.0, 0.0, 0.5)
   ! 3.66312787E-02
 
-  ! probability density at x=2.0 with lambda=-1.0 (out of range)
-  print *, exp_pdf(2.0, -1.0) 
+  ! probability density at x=1.5 with loc=0.5 and scale=0.5 (lambda=2.0)
+  print *, exp_pdf(2.5, 0.5, 0.5)
+  ! 3.66312787E-02
+
+  ! probability density at x=2.0 with loc=0.0 and scale=-1.0 (out of range)
+  print *, exp_pdf(2.0, 0.0, -1.0)
   ! NaN
 
-  ! standard exponential random variates array  
-  x = reshape(rexp(0.5, 24), [2, 3, 4])
+  ! standard exponential random variates array
+  x = reshape(rexp(0.0, 2.0, 24), [2, 3, 4])
 
   ! a rank-3 exponential probability density
-  lambda(:, :, :) = 0.5
-  print *, exp_pdf(x, lambda)
+  loc(:, :, :)   = 0.0
+  scale(:, :, :) = 2.0
+  print *, exp_pdf(x, loc, scale)
   ! 0.349295378      0.332413018     0.470253497     0.443498343      0.317152828
   ! 0.208242029      0.443112582     8.07073265E-02  0.245337561      0.436016470
   ! 7.14025944E-02   5.33841923E-02  0.322308093     0.264558554      0.212898195
   ! 0.100339092      0.226891592     0.444002301     9.91026312E-02   3.87373678E-02
-  ! 3.11400592E-02   0.349431813     0.482774824     0.432669312     
+  ! 3.11400592E-02   0.349431813     0.482774824     0.432669312
 
-  ! probability density array where lambda<=0.0 for certain elements 
-  print *, exp_pdf([1.0, 1.0, 1.0], [1.0, 0.0, -1.0])
+  ! probability density array where scale<=0.0 for certain elements (loc = 0.0)
+  print *, exp_pdf([1.0, 1.0, 1.0], [0.0, 0.0, 0.0], [1.0, 0.0, -1.0])
   ! 0.367879450  NaN NaN
 
-  ! `pdf_exp` is pure and, thus, can be called concurrently 
+  ! `pdf_exp` is pure and, thus, can be called concurrently
   xsum = 0.0
   do concurrent (i=1:size(x,3))
-    xsum = xsum + sum(exp_pdf(x(:,:,i), lambda(:,:,i)))
+    xsum = xsum + sum(exp_pdf(x(:,:,i), loc(:,:,i), scale(:,:,i)))
   end do
   print *, xsum
   ! 6.45566940
 
-  ! complex exponential probability density function at (1.5,1.0) with real part
-  ! of lambda=1.0 and imaginary part of lambda=2.0
-  scale = (1.0, 2.)
-  print *, exp_pdf((1.5, 1.0), scale)
+  ! complex exponential probability density function at (1.5, 0.0, 1.0) with real part
+  ! of scale=1.0 and imaginary part of scale=0.5
+  cloc   = (0.0, 0.0)
+  cscale = (1.0, 0.5)
+  print *, exp_pdf((1.5, 1.0), cloc, cscale)
   ! 6.03947677E-02
 
-  ! As above, but with lambda%re < 0 
-  scale = (-1.0, 2.)
-  print *, exp_pdf((1.5, 1.0), scale)
+  ! As above, but with scale%re < 0
+  cloc   = (0.0, 0.0)
+  cscale = (-1.0, 2.0)
+  print *, exp_pdf((1.5, 1.0), cloc, cscale)
   ! NaN
 
 end program example_exponential_pdf
diff --git a/example/stats_distribution_exponential/example_exponential_rvs.f90 b/example/stats_distribution_exponential/example_exponential_rvs.f90
index 551d2fdce..af189f109 100644
--- a/example/stats_distribution_exponential/example_exponential_rvs.f90
+++ b/example/stats_distribution_exponential/example_exponential_rvs.f90
@@ -3,30 +3,28 @@ program example_exponential_rvs
   use stdlib_stats_distribution_exponential, only: rexp => rvs_exp
 
   implicit none
-  complex :: scale
+  complex :: cloc, cscale
   integer :: seed_put, seed_get
 
   seed_put = 1234567
   call random_seed(seed_put, seed_get)
 
   print *, rexp()         !single standard exponential random variate
-
 ! 0.358690143
 
-  print *, rexp(2.0)       !exponential random variate with lambda=2.0
-
-! 0.816459715
-
-  print *, rexp(0.3, 10)   !an array of 10 variates with lambda=0.3
+  print *, rexp(0.6, 0.2) !exponential random variate with loc=0.6 and scale=0.5 (lambda=2)
+! 0.681645989
 
-!  1.84008647E-02  3.59742008E-02  0.136567295  0.262772143  3.62352766E-02
-!  0.547133625  0.213591918  4.10784185E-02  0.583882213  0.671128035
+  print *, rexp(0.0, 3.0, 10)   !an array of 10 variates with loc=0.0 and scale=3.0 (lambda=1/3)
+! 0.184008643      0.359742016       1.36567295       2.62772131      0.362352759
+! 5.47133636       2.13591909      0.410784155       5.83882189       6.71128035
 
-  scale = (2.0, 0.7)
-  print *, rexp(scale)
-!single complex exponential random variate with real part of lambda=2.0;
-!imagainary part of lambda=0.7
+  cloc   = (0.0, 0.0)
+  cscale = (0.5, 1.6)
+  print *, rexp(cloc, cscale)
+!single complex exponential random variate with real part of scale=0.5 (lambda=2.0);
+!imagainary part of scale=1.6 (lambda=0.625)
 
-! (1.41435969,4.081114382E-02)
+! (0.219550118,1.01847279)
 
 end program example_exponential_rvs
diff --git a/src/stdlib_stats_distribution_exponential.fypp b/src/stdlib_stats_distribution_exponential.fypp
index 7e3a43ae4..ffebb3299 100644
--- a/src/stdlib_stats_distribution_exponential.fypp
+++ b/src/stdlib_stats_distribution_exponential.fypp
@@ -114,7 +114,7 @@ contains
     #:for k1, t1 in REAL_KINDS_TYPES
     impure function rvs_exp_0_${t1[0]}$${k1}$( ) result(res)
     !
-    ! Standard exponential random variate (lambda=1)
+    ! Standard exponential random variate (lambda=1; scale=1/lambda=1)
     !
         ${t1}$ :: res, x
         ${t1}$, parameter :: r = 7.69711747013104972_${k1}$
@@ -153,18 +153,18 @@ contains
 
 
     #:for k1, t1 in REAL_KINDS_TYPES
-    impure elemental function rvs_exp_${t1[0]}$${k1}$(lambda) result(res)
+    impure elemental function rvs_exp_${t1[0]}$${k1}$(loc, scale) result(res)
     !
     ! Exponential distributed random variate
     !
-        ${t1}$, intent(in) :: lambda
+        ${t1}$, intent(in) :: loc, scale
         ${t1}$ :: res
 
-        if (lambda <= 0._${k1}$) then
+        if (scale <= 0._${k1}$) then
             res = ieee_value(1._${k1}$, ieee_quiet_nan)
         else
             res = rvs_exp_0_${t1[0]}$${k1}$(  )
-            res = res / lambda
+            res = res * scale + loc
         end if
     end function rvs_exp_${t1[0]}$${k1}$
 
@@ -174,13 +174,13 @@ contains
 
 
     #:for k1, t1 in CMPLX_KINDS_TYPES
-    impure elemental function rvs_exp_${t1[0]}$${k1}$(lambda) result(res)
-        ${t1}$, intent(in) :: lambda
+    impure elemental function rvs_exp_${t1[0]}$${k1}$(loc, scale) result(res)
+        ${t1}$, intent(in) :: loc, scale
         ${t1}$ :: res
         real(${k1}$) :: tr, ti
 
-        tr = rvs_exp_r${k1}$(lambda % re)
-        ti = rvs_exp_r${k1}$(lambda % im)
+        tr = rvs_exp_r${k1}$(loc%re, scale%re)
+        ti = rvs_exp_r${k1}$(loc%im, scale%im)
         res = cmplx(tr, ti, kind=${k1}$)
     end function rvs_exp_${t1[0]}$${k1}$
 
@@ -190,14 +190,14 @@ contains
 
 
     #:for k1, t1 in REAL_KINDS_TYPES
-    impure function rvs_exp_array_${t1[0]}$${k1}$(lambda, array_size) result(res)
-        ${t1}$, intent(in) :: lambda
+    impure function rvs_exp_array_${t1[0]}$${k1}$(loc, scale, array_size) result(res)
+        ${t1}$, intent(in) :: loc, scale
         integer, intent(in) :: array_size
         ${t1}$ :: res(array_size), x, re
         ${t1}$, parameter :: r = 7.69711747013104972_${k1}$
         integer :: jz, iz, i
 
-        if (lambda <= 0._${k1}$) then
+        if (scale <= 0._${k1}$) then
             res = ieee_value(1._${k1}$, ieee_quiet_nan)
             return
         end if
@@ -228,7 +228,7 @@ contains
                     end if
                end do L1
             endif
-            res(i) = re / lambda
+            res(i) = re * scale + loc
         end do
     end function rvs_exp_array_${t1[0]}$${k1}$
 
@@ -238,16 +238,16 @@ contains
 
 
     #:for k1, t1 in CMPLX_KINDS_TYPES
-    impure function rvs_exp_array_${t1[0]}$${k1}$(lambda, array_size) result(res)
-        ${t1}$, intent(in) :: lambda
+    impure function rvs_exp_array_${t1[0]}$${k1}$(loc, scale, array_size) result(res)
+        ${t1}$, intent(in) :: loc, scale
         integer, intent(in) :: array_size
         ${t1}$ :: res(array_size)
         integer :: i
         real(${k1}$) :: tr, ti
 
         do i = 1, array_size
-            tr = rvs_exp_r${k1}$(lambda % re)
-            ti = rvs_exp_r${k1}$(lambda % im)
+            tr = rvs_exp_r${k1}$(loc%re, scale%re)
+            ti = rvs_exp_r${k1}$(loc%im, scale%im)
             res(i) = cmplx(tr, ti, kind=${k1}$)
         end do
     end function rvs_exp_array_${t1[0]}$${k1}$
@@ -258,19 +258,19 @@ contains
 
 
     #:for k1, t1 in REAL_KINDS_TYPES
-    elemental function pdf_exp_${t1[0]}$${k1}$(x, lambda) result(res)
+    elemental function pdf_exp_${t1[0]}$${k1}$(x, loc, scale) result(res)
     !
     ! Exponential Distribution Probability Density Function
     !
-        ${t1}$, intent(in) :: x, lambda
+        ${t1}$, intent(in) :: x, loc, scale
         real(${k1}$) :: res
 
-        if (lambda <= 0._${k1}$) then
+        if (scale <= 0._${k1}$) then
             res = ieee_value(1._${k1}$, ieee_quiet_nan)
-        else if (x < 0._${k1}$) then
+        else if (x < loc) then
             res = 0._${k1}$
         else
-            res = exp(- x * lambda) * lambda
+            res = exp(- (x - loc) / scale) / scale
         end if
     end function pdf_exp_${t1[0]}$${k1}$
 
@@ -280,12 +280,12 @@ contains
 
 
     #:for k1, t1 in CMPLX_KINDS_TYPES
-    elemental function pdf_exp_${t1[0]}$${k1}$(x, lambda) result(res)
-        ${t1}$, intent(in) :: x, lambda
+    elemental function pdf_exp_${t1[0]}$${k1}$(x, loc, scale) result(res)
+        ${t1}$, intent(in) :: x, loc, scale
         real(${k1}$) :: res
 
-        res = pdf_exp_r${k1}$(x % re, lambda % re)
-        res = res * pdf_exp_r${k1}$(x % im, lambda % im)
+        res = pdf_exp_r${k1}$(x%re, loc%re, scale%re)
+        res = res * pdf_exp_r${k1}$(x%im, loc%im, scale%im)
     end function pdf_exp_${t1[0]}$${k1}$
 
     #:endfor
@@ -294,19 +294,19 @@ contains
 
 
     #:for k1, t1 in REAL_KINDS_TYPES
-    elemental function cdf_exp_${t1[0]}$${k1}$(x, lambda) result(res)
+    elemental function cdf_exp_${t1[0]}$${k1}$(x, loc, scale) result(res)
     !
     ! Exponential Distribution Cumulative Distribution Function
     !
-        ${t1}$, intent(in) :: x, lambda
+        ${t1}$, intent(in) :: x, loc, scale
         real(${k1}$) :: res
 
-        if (lambda <= 0._${k1}$) then
+        if (scale <= 0._${k1}$) then
             res = ieee_value(1._${k1}$, ieee_quiet_nan)
-        else if (x < 0._${k1}$) then
+        else if (x < loc) then
             res = 0._${k1}$
         else
-            res = 1.0_${k1}$ - exp(- x * lambda)
+            res = 1.0_sp - exp(- (x - loc) / scale)
         end if
     end function cdf_exp_${t1[0]}$${k1}$
 
@@ -316,12 +316,12 @@ contains
 
 
     #:for k1, t1 in CMPLX_KINDS_TYPES
-    elemental function cdf_exp_${t1[0]}$${k1}$(x, lambda) result(res)
-        ${t1}$, intent(in) :: x, lambda
+    elemental function cdf_exp_${t1[0]}$${k1}$(x, loc, scale) result(res)
+        ${t1}$, intent(in) :: x, loc, scale
         real(${k1}$) :: res
 
-        res = cdf_exp_r${k1}$(x % re, lambda % re)
-        res = res * cdf_exp_r${k1}$(x % im, lambda % im)
+        res = cdf_exp_r${k1}$(x%re, loc%re, scale%re)
+        res = res * cdf_exp_r${k1}$(x%im, loc%im, scale%im)
     end function cdf_exp_${t1[0]}$${k1}$
 
     #:endfor
diff --git a/test/stats/test_distribution_exponential.fypp b/test/stats/test_distribution_exponential.fypp
index 01d3f5bb5..5df3b29fb 100644
--- a/test/stats/test_distribution_exponential.fypp
+++ b/test/stats/test_distribution_exponential.fypp
@@ -53,7 +53,7 @@ contains
         print *, "Test exponential random generator with chi-squared"
         freq = 0
         do i = 1, num
-            j = 1000 * (1 - exp(- expon_rvs(1.0)))
+            j = 1000 * (1 - exp(- expon_rvs(0.0, 1.0)))
             freq(j) = freq(j) + 1
         end do
         chisq = 0.0_dp
@@ -72,46 +72,46 @@ contains
 
     #:for k1, t1 in RC_KINDS_TYPES
     subroutine test_expon_rvs_${t1[0]}$${k1}$
-        ${t1}$ :: res(10), scale
+        ${t1}$ :: res(10), loc, scale
         integer, parameter :: k = 5
         integer :: i
         integer :: seed, get
         #:if t1[0] == "r"
             #! for real type
         ${t1}$, parameter :: ans(10) =                                         &
-                            [0.609680481289574416337018192280083895_${k1}$,    &
-                             0.137541023585612635452927558314210417_${k1}$,    &
-                             0.134921508232253721063879462841820585_${k1}$,    &
-                              1.33766060689229752493171569464417802_${k1}$,    &
-                             0.111148487576340881943792737729381770_${k1}$,    &
-                             0.533951653963536868966836361020492979_${k1}$,    &
-                              1.96897428558727671799033487332053483_${k1}$,    &
-                             0.371111977992924465160247867364281152_${k1}$,    &
-                             0.811918715695663687862785688290993341_${k1}$,    &
-                             0.404637854946697868759504975362991277_${k1}$]
+                            [ 1.37178108290154243675829093263018876_${k1}$,    &
+                             0.309467303067628429769087006206973456_${k1}$,    &
+                             0.303573393522570872393728791394096334_${k1}$,    &
+                              3.00973636550766943109636031294940040_${k1}$,    &
+                             0.250084097046766984373533659891108982_${k1}$,    &
+                              1.20139122141795795517538181229610927_${k1}$,    &
+                              4.43019214257137261547825346497120336_${k1}$,    &
+                             0.835001950484080046610557701569632627_${k1}$,    &
+                              1.82681711031524329769126779865473509_${k1}$,    &
+                             0.910435173630070204708886194566730410_${k1}$]
         #:else
             #! for complex type
         ${t1}$, parameter :: ans(10) =                                         &
-                            [(1.30645817419194517786503898345732266_${k1}$,    &
-                             0.158701181060322271676454874977935106_${k1}$),   &
-                            (0.289117517640543687994027420375329869_${k1}$,    &
-                              1.54345454641418945184428733997405138_${k1}$),   &
-                            (0.238175330520730461308127295134389521_${k1}$,    &
-                             0.616098062265619464192503493485184250_${k1}$),   &
-                             (4.21923061197273582426500329997257485_${k1}$,    &
-                             0.428206128453374382877209077728016710_${k1}$),   &
-                             (1.73982581934785075970596933205212874_${k1}$,    &
-                             0.466889832630805233184044202341912994_${k1}$),   &
-                             (2.22649889847873832288931745486999202_${k1}$,    &
-                             0.879109337848515628785697537331053851_${k1}$),   &
-                             (8.76802198822945553859296653951917464_${k1}$,    &
-                             0.200128045239398311139211728004738688_${k1}$),   &
-                            (0.694821947760945587572020290930855262_${k1}$,    &
-                             0.101964167346166995492113143812345625_${k1}$),   &
-                            (0.141476585024528208770330398432893829_${k1}$,    &
-                       3.989655879458742013468417133900891716E-0002_${k1}$),   &
-                             (2.10676792861163792685325850990401309_${k1}$,    &
-                             0.249356813451327473065187125310051027_${k1}$)]
+                            [(0.640164505354053137153869101894088070_${k1}$,   &
+                              0.268204995991944639133208738712710328_${k1}$),  &
+                             (0.141667583643866407117073435983911608_${k1}$,   &
+                               2.60843818343998017361684560455614716_${k1}$),  &
+                             (0.116705911955157926040982374615850854_${k1}$,   &
+                               1.04120572522889689448533090398996145_${k1}$),  &
+                              (2.06742299986664055388985161698656149_${k1}$,   &
+                              0.723668357086202707062483341360348315_${k1}$),  &
+                             (0.852514651480446872255924972705542983_${k1}$,   &
+                              0.789043817146060844081034701957833041_${k1}$),  &
+                              (1.09098446025458177821576555288629603_${k1}$,   &
+                               1.48569478096399141264782883808948111_${k1}$),  &
+                              (4.29633077423243321391055360436439499_${k1}$,   &
+                              0.338216396454583145825267820328008412_${k1}$),  &
+                             (0.340462754402863337910289942556119029_${k1}$,   &
+                              0.172319442815022222381671213042864120_${k1}$),  &
+                       (6.932352666201882229746189523211795805E-0002_${k1}$,   &
+                        6.742518436285274002761624956292507704E-0002_${k1}$),  &
+                              (1.03231628501970258415809666985296648_${k1}$,   &
+                              0.421413014732743429480166241773986277_${k1}$)]
         #:endif
 
         print *, "Test exponential_distribution_rvs_${t1[0]}$${k1}$"
@@ -120,16 +120,18 @@ contains
 
         #:if t1[0] == "r"
             #! for real type
+        loc   = 0.0_${k1}$
         scale = 1.5_${k1}$
         #:else
             #! for complex type
+        loc   = (0.0_${k1}$, 0.0_${k1}$)
         scale = (0.7_${k1}$, 1.3_${k1}$)
         #:endif
 
         do i = 1, k
-            res(i) = expon_rvs(scale)      ! 1 dummy
+            res(i) = expon_rvs(loc, scale)      ! 1 dummy
         end do
-        res(6:10) = expon_rvs(scale, k)    ! 2 dummies
+        res(6:10) = expon_rvs(loc, scale, k)    ! 2 dummies
         call check(all(abs(res - ans) < ${k1}$tol),                            &
             msg="exponential_distribution_rvs_${t1[0]}$${k1}$ failed", warn=warn)
     end subroutine test_expon_rvs_${t1[0]}$${k1}$
@@ -142,45 +144,45 @@ contains
     #:for k1, t1 in RC_KINDS_TYPES
     subroutine test_expon_pdf_${t1[0]}$${k1}$
 
-        ${t1}$ :: x1, x2(3,4), scale
+        ${t1}$ :: x1, x2(3,4), loc, scale
         integer :: seed, get
         real(${k1}$) :: res(3,5)
         #:if t1[0] == "r"
             #! for real type
         real(${k1}$), parameter :: ans(15) =                                   &
-                             [0.362692289054629718342313806171796533_${k1}$,   &
-                              0.362692289054629718342313806171796533_${k1}$,   &
-                              0.362692289054629718342313806171796533_${k1}$,   &
-                               1.44877092399186122284289290051705535_${k1}$,   &
-                               1.08871761038277651996081144393335589_${k1}$,   &
-                              0.203258408490339213767867275283195750_${k1}$,   &
-                              0.730004225568590859263284124264208147_${k1}$,   &
-                              0.237394827760488451509080387833146683_${k1}$,   &
-                              0.301732182586179598102005265289645959_${k1}$,   &
-                               1.35079274124711914255014934401469271_${k1}$,   &
-                              0.416578245043239337295928202660090263_${k1}$,   &
-                               1.44039177901335374382803898226703593_${k1}$,   &
-                              0.196044829271295768265275728683411055_${k1}$,   &
-                              0.271373826917613661285112379170965958_${k1}$,   &
-                               1.00108987409617105109732206933052664_${k1}$]
+                             [0.161196572913168763707695024965242901_${k1}$,   &
+                              0.161196572913168763707695024965242901_${k1}$,   &
+                              0.161196572913168763707695024965242901_${k1}$,   &
+                              0.643898188440827210152396844674246781_${k1}$,   &
+                              0.483874493503456231093693975081491447_${k1}$,   &
+                         9.03370704401507616746076779036425611E-0002_${k1}$,   &
+                              0.324446322474929270783681833006314743_${k1}$,   &
+                              0.105508812337994867337369061259176307_${k1}$,   &
+                              0.134103192260524265823113451239842656_${k1}$,   &
+                              0.600352329443164063355621930673196730_${k1}$,   &
+                              0.185145886685884149909301423404484569_${k1}$,   &
+                              0.640174124005934997256906214340904849_${k1}$,   &
+                         8.71310352316870081179003238592937984E-0002_${k1}$,   &
+                              0.120610589741161627237827724075984870_${k1}$,   &
+                              0.444928832931631578265476475258011855_${k1}$]
         #:else
             #! for complex type
         real(${k1}$), parameter :: ans(15) =                                   &
-                             [0.112097715784191810518066563334849515_${k1}$,   &
-                              0.112097715784191810518066563334849515_${k1}$,   &
-                              0.112097715784191810518066563334849515_${k1}$,   &
-                         4.72087485401191174735651518020251204E-0002_${k1}$,   &
-                         3.69705018439006691768174449531170720E-0002_${k1}$,   &
-                         8.69498969681198520061798177185735738E-0002_${k1}$,   &
-                              0.128007654288233028296342302153338001_${k1}$,   &
-                         1.13496395875758374774198906169957218E-0002_${k1}$,   &
-                              0.294260498264128747413785056084385424_${k1}$,   &
-                         4.66169813179250908948018478030960097E-0002_${k1}$,   &
-                         2.84438693906889813143446828488861951E-0002_${k1}$,   &
-                              0.161859307815385236742977105439660254_${k1}$,   &
-                         4.22904796362406579112752522035325397E-0002_${k1}$,   &
-                              0.176117981883470250164040199296778089_${k1}$,   &
-                              0.107352342201327219885025541854724060_${k1}$]
+                             [0.486535224757776955373552792251950892_${k1}$,   &
+                              0.486535224757776955373552792251950892_${k1}$,   &
+                              0.486535224757776955373552792251950892_${k1}$,   &
+                              0.204899082205378114034570971362956231_${k1}$,   &
+                              0.160462247586374432191047938164570635_${k1}$,   &
+                              0.377386705590797968776822125514642235_${k1}$,   &
+                              0.555588777292678074202874575318307322_${k1}$,   &
+                         4.92605884877423501624127196918217120E-0002_${k1}$,   &
+                               1.27717230149361435509455319481070053_${k1}$,   &
+                              0.202330648081272095897577464423159785_${k1}$,   &
+                              0.123454294230420925843509908198290816_${k1}$,   &
+                              0.702514356837609534474727020137414207_${k1}$,   &
+                              0.183552428976738966628798837688943286_${k1}$,   &
+                              0.764400963035895183003646698336710458_${k1}$,   &
+                              0.465938985248816058528756692077795393_${k1}$]
         #:endif
 
         print *, "Test exponential_distribution_pdf_${t1[0]}$${k1}$"
@@ -188,16 +190,18 @@ contains
         call random_seed(seed, get)
         #:if t1[0] == "r"
             #! for real type
+        loc   = 0.0_${k1}$
         scale = 1.5_${k1}$
         #:else
             #! for complex type
+        loc   = (0.0_${k1}$, 0.0_${k1}$)
         scale = (0.3_${k1}$, 1.6_${k1}$)
         #:endif
 
-        x1 = expon_rvs(scale)
-        x2 = reshape(expon_rvs(scale, 12), [3,4])
-        res(:,1) = expon_pdf(x1, scale)
-        res(:, 2:5) = expon_pdf(x2, scale)
+        x1 = expon_rvs(loc, scale)
+        x2 = reshape(expon_rvs(loc, scale, 12), [3,4])
+        res(:,1) = expon_pdf(x1, loc, scale)
+        res(:, 2:5) = expon_pdf(x2, loc, scale)
         call check(all(abs(res - reshape(ans, [3,5])) < ${k1}$tol),            &
             msg="exponential_distribution_pdf_${t1[0]}$${k1}$ failed", warn=warn)
     end subroutine test_expon_pdf_${t1[0]}$${k1}$
@@ -210,7 +214,7 @@ contains
     #:for k1, t1 in RC_KINDS_TYPES
     subroutine test_expon_cdf_${t1[0]}$${k1}$
 
-        ${t1}$ :: x1, x2(3,4), scale
+        ${t1}$ :: x1, x2(3,4), loc, scale
         integer :: seed, get
         real(${k1}$) :: res(3,5)
         #:if t1[0] == "r"
@@ -256,15 +260,17 @@ contains
 
         #:if t1[0] == "r"
             #! for real type
+        loc   = 0.0_${k1}$
         scale = 2.0_${k1}$
         #:else
+        loc   = (0.0_${k1}$, 0.0_${k1}$)
         scale = (1.3_${k1}$, 2.1_${k1}$)
         #:endif
 
-        x1 = expon_rvs(scale)
-        x2 = reshape(expon_rvs(scale, 12), [3,4])
-        res(:,1) = expon_cdf(x1, scale)
-        res(:, 2:5) = expon_cdf(x2, scale)
+        x1 = expon_rvs(loc, scale)
+        x2 = reshape(expon_rvs(loc, scale, 12), [3,4])
+        res(:,1) = expon_cdf(x1, loc, scale)
+        res(:, 2:5) = expon_cdf(x2, loc, scale)
         call check(all(abs(res - reshape(ans,[3,5])) < ${k1}$tol),             &
             msg="exponential_distribution_cdf_${t1[0]}$${k1}$ failed", warn=warn)
     end subroutine test_expon_cdf_${t1[0]}$${k1}$

From e7984cb93a97dbebce57f73d622afc3215e3aa4f Mon Sep 17 00:00:00 2001
From: Sebastian <sebastian@mutz.science>
Date: Tue, 13 May 2025 19:12:16 +0100
Subject: [PATCH 2/7] reintroduced old interface through wrappers and updated
 specs

---
 .../stdlib_stats_distribution_exponential.md  |  60 ++++-
 .../example_exponential_cdf.f90               |   8 +
 .../example_exponential_pdf.f90               |  10 +-
 .../example_exponential_rvs.f90               |  32 ++-
 ...stdlib_stats_distribution_exponential.fypp | 171 +++++++++++++-
 test/stats/test_distribution_exponential.fypp | 222 +++++++++++-------
 6 files changed, 399 insertions(+), 104 deletions(-)

diff --git a/doc/specs/stdlib_stats_distribution_exponential.md b/doc/specs/stdlib_stats_distribution_exponential.md
index b11ca6a6c..27f5919a4 100644
--- a/doc/specs/stdlib_stats_distribution_exponential.md
+++ b/doc/specs/stdlib_stats_distribution_exponential.md
@@ -15,14 +15,19 @@ Experimental
 ### Description
 
 An exponential distribution is the distribution of time between events in a Poisson point process.
-The inverse scale parameter `lambda` specifies the average time between events (\(\lambda\)), also called the rate of events.
+The inverse `scale` parameter `lambda` specifies the average time between events (\(\lambda\)), also called the rate of events. The location `loc` specifies the value by which the distribution is shifted.
 
-Without argument, the function returns a random sample from the standard exponential distribution \(E(\lambda=1)\).
+Without argument, the function returns a random sample from the unshifted standard exponential distribution \(E(\lambda=1)\) or \(E(loc=0, scale=1)\).
 
-With a single argument, the function returns a random sample from the exponential distribution \(E(\lambda=\text{lambda})\).
+With a single argument of type `real`, the function returns a random sample from the exponential distribution \(E(\lambda=\text{lambda})\). 
 For complex arguments, the real and imaginary parts are sampled independently of each other.
 
-With two arguments, the function returns a rank-1 array of exponentially distributed random variates.
+With one argument of type `real` and one argument of type `integer`, the function returns a rank-1 array of exponentially distributed random variates for (E(\lambda=\text{lambda})\).
+
+With two arguments of type `real`, the function returns a random sample from the exponential distribution \(E(loc=loc, scale=scale)\).
+For complex arguments, the real and imaginary parts are sampled independently of each other.
+
+With two arguments of type `real` and one argument of type `integer`, the function returns a rank-1 array of exponentially distributed random variates for \(E(loc=loc, scale=scale)\).
 
 @note
 The algorithm used for generating exponential random variates is fundamentally limited to double precision.[^1]
@@ -31,6 +36,10 @@ The algorithm used for generating exponential random variates is fundamentally l
 
 `result = ` [[stdlib_stats_distribution_exponential(module):rvs_exp(interface)]] `([lambda] [[, array_size]])`
 
+or
+
+`result = ` [[stdlib_stats_distribution_exponential(module):rvs_exp(interface)]] `([loc, scale] [[, array_size]])`
+
 ### Class
 
 Elemental function
@@ -40,13 +49,21 @@ Elemental function
 `lambda`: optional argument has `intent(in)` and is a scalar of type `real` or `complex`.
 If `lambda` is `real`, its value must be positive. If `lambda` is `complex`, both the real and imaginary components must be positive.
 
+`loc`: optional argument has `intent(in)` and is a scalar of type `real` or `complex`. 
+
+`scale`: optional argument has `intent(in)` and is a positive scalar of type `real` or `complex`.
+If `scale` is `real`, its value must be positive. If `scale` is `complex`, both the real and imaginary components must be positive.
+
 `array_size`: optional argument has `intent(in)` and is a scalar of type `integer` with default kind.
 
 ### Return value
 
-The result is a scalar or rank-1 array with a size of `array_size`, and the same type as `lambda`.
+If `lambda` is passed, the result is a scalar or rank-1 array with a size of `array_size`, and the same type as `lambda`.
 If `lambda` is non-positive, the result is `NaN`.
 
+If `loc` and `scale` are passed, the result is a scalar or rank-1 array with a size of `array_size`, and the same type as `scale`.
+If `scale` is non-positive, the result is `NaN`.
+
 ### Example
 
 ```fortran
@@ -69,10 +86,16 @@ For a complex variable \(z=(x + y i)\) with independent real \(x\) and imaginary
 
 $$f(x+\mathit{i}y)=f(x)f(y)=\begin{cases} \lambda_{x} \lambda_{y} e^{-(\lambda_{x} x + \lambda_{y} y)} &x\geqslant 0, y\geqslant 0 \\\\ 0 &\text{otherwise}\end{cases}$$
 
+Instead of of the inverse scale parameter `lambda`, it is possible to pass `loc` and `scale`, where \(scale = \frac{1}{\lambda}\) and `loc` specifies the value by which the distribution is shifted.
+
 ### Syntax
 
 `result = ` [[stdlib_stats_distribution_exponential(module):pdf_exp(interface)]] `(x, lambda)`
 
+or
+
+`result = ` [[stdlib_stats_distribution_exponential(module):pdf_exp(interface)]] `(x, loc, scale)`
+
 ### Class
 
 Elemental function
@@ -84,11 +107,20 @@ Elemental function
 `lambda`: has `intent(in)` and is a scalar of type `real` or `complex`.
 If `lambda` is `real`, its value must be positive. If `lambda` is `complex`, both the real and imaginary components must be positive.
 
+`loc`: has `intent(in)` and is a scalar of type `real` or `complex`.
+
+`scale`: has `intent(in)` and is a positive scalar of type `real` or `complex`.
+If `scale` is `real`, its value must be positive. If `scale` is `complex`, both the real and imaginary components must be positive.
+
 All arguments must have the same type.
 
 ### Return value
 
-The result is a scalar or an array, with a shape conformable to the arguments, and the same type as the input arguments. If `lambda` is non-positive, the result is `NaN`.
+If `lambda` is passed, the result is a scalar or an array, with a shape conformable to the arguments, and the same type as the input arguments. If `lambda` is non-positive, the result is `NaN`.
+
+
+If `loc` and `scale` are passed, the result is a scalar or an array, with a shape conformable to the arguments, and the same type as the input arguments. If `scale` is non-positive, the result is `NaN`.
+
 
 ### Example
 
@@ -112,10 +144,16 @@ For a complex variable  \(z=(x + y i)\) with independent real \(x\) and imaginar
 
 $$F(x+\mathit{i}y)=F(x)F(y)=\begin{cases} (1 - e^{-\lambda_{x} x})(1 - e^{-\lambda_{y} y}) &x\geqslant 0, \;\; y\geqslant 0 \\\\ 0 & \text{otherwise} \end{cases}$$
 
+Instead of of the inverse scale parameter `lambda`, it is possible to pass `loc` and `scale`, where \(scale = \frac{1}{\lambda}\) and `loc` specifies the value by which the distribution is shifted.
+
 ### Syntax
 
 `result = ` [[stdlib_stats_distribution_exponential(module):cdf_exp(interface)]] `(x, lambda)`
 
+or
+
+`result = ` [[stdlib_stats_distribution_exponential(module):cdf_exp(interface)]] `(x, loc, scale)`
+
 ### Class
 
 Elemental function
@@ -127,11 +165,19 @@ Elemental function
 `lambda`: has `intent(in)` and is a scalar of type `real` or `complex`.
 If `lambda` is `real`, its value must be positive. If `lambda` is `complex`, both the real and imaginary components must be positive.
 
+`loc`: has `intent(in)` and is a scalar of type `real` or `complex`.
+
+`scale`: has `intent(in)` and is a positive scalar of type `real` or `complex`.
+If `scale` is `real`, its value must be positive. If `scale` is `complex`, both the real and imaginary components must be positive.
+
 All arguments must have the same type.
 
 ### Return value
 
-The result is a scalar or an array, with a shape conformable to the arguments, and the same type as the input arguments. If `lambda` is non-positive, the result is `NaN`.
+If `lamba` is passed, the result is a scalar or an array, with a shape conformable to the arguments, and the same type as the input arguments. If `lambda` is non-positive, the result is `NaN`.
+
+
+If `loc` and `scale` are passed, the result is a scalar or an array, with a shape conformable to the arguments, and the same type as the input arguments. If `scale` is non-positive, the result is `NaN`.
 
 ### Example
 
diff --git a/example/stats_distribution_exponential/example_exponential_cdf.f90 b/example/stats_distribution_exponential/example_exponential_cdf.f90
index f319662c4..e99edaed9 100644
--- a/example/stats_distribution_exponential/example_exponential_cdf.f90
+++ b/example/stats_distribution_exponential/example_exponential_cdf.f90
@@ -12,10 +12,18 @@ program example_exponential_cdf
   seed_put = 1234567
   call random_seed(seed_put, seed_get)
 
+  ! standard exponential cumulative distribution at x=1.0 with lambda=1.0
+  print *, exp_cdf(1.0, 1.0)
+  ! 0.632120550
+
   ! standard exponential cumulative distribution at x=1.0 with loc=0.0, scale=1.0
   print *, exp_cdf(1.0, 0.0, 1.0)
   ! 0.632120550
 
+  ! cumulative distribution at x=2.0 with lambda=2
+  print *, exp_cdf(2.0, 2.0)
+  ! 0.981684387
+
   ! cumulative distribution at x=2.0 with loc=0.0 and scale=0.5 (equivalent of lambda=2)
   print *, exp_cdf(2.0, 0.0, 0.5)
   ! 0.981684387
diff --git a/example/stats_distribution_exponential/example_exponential_pdf.f90 b/example/stats_distribution_exponential/example_exponential_pdf.f90
index 3f4ef6c2e..c8f9aa379 100644
--- a/example/stats_distribution_exponential/example_exponential_pdf.f90
+++ b/example/stats_distribution_exponential/example_exponential_pdf.f90
@@ -12,10 +12,18 @@ program example_exponential_pdf
   seed_put = 1234567
   call random_seed(seed_put, seed_get)
 
-  ! probability density at x=1.0 with loc=0 and in standard exponential
+  ! probability density at x=1.0 with lambda=1.0
+  print *, exp_pdf(1.0, 1.0)
+  ! 0.367879450
+
+  ! probability density at x=1.0 with loc=0 and scale=1.0
   print *, exp_pdf(1.0, 0.0, 1.0)
   ! 0.367879450
 
+  ! probability density at x=2.0 with lambda=2.0
+  print *, exp_pdf(2.0, 2.0)
+  ! 3.66312787E-02
+
   ! probability density at x=2.0 with loc=0.0 and scale=0.5 (lambda=2.0)
   print *, exp_pdf(2.0, 0.0, 0.5)
   ! 3.66312787E-02
diff --git a/example/stats_distribution_exponential/example_exponential_rvs.f90 b/example/stats_distribution_exponential/example_exponential_rvs.f90
index af189f109..65fa84a65 100644
--- a/example/stats_distribution_exponential/example_exponential_rvs.f90
+++ b/example/stats_distribution_exponential/example_exponential_rvs.f90
@@ -9,22 +9,32 @@ program example_exponential_rvs
   seed_put = 1234567
   call random_seed(seed_put, seed_get)
 
-  print *, rexp()         !single standard exponential random variate
-! 0.358690143
+ ! single standard exponential random variate
+  print *, rexp()
+  ! 0.358690143
 
-  print *, rexp(0.6, 0.2) !exponential random variate with loc=0.6 and scale=0.5 (lambda=2)
-! 0.681645989
+  ! exponential random variate with lambda=2
+   print *, rexp(2.0)
+  ! 0.204114929
 
-  print *, rexp(0.0, 3.0, 10)   !an array of 10 variates with loc=0.0 and scale=3.0 (lambda=1/3)
-! 0.184008643      0.359742016       1.36567295       2.62772131      0.362352759
-! 5.47133636       2.13591909      0.410784155       5.83882189       6.71128035
+  ! exponential random variate with loc=0 and scale=0.5 (lambda=2)
+  print *, rexp(0.0, 0.5)
+  ! 0.122672431
 
+  ! exponential random variate with loc=0.6 and scale=0.2 (lambda=5)
+  print *, rexp(0.6, 0.2)
+  ! 0.681645989
+
+  ! an array of 10 variates with loc=0.0 and scale=3.0 (lambda=1/3)
+  print *, rexp(0.0, 3.0, 10)
+  ! 1.36567295       2.62772131      0.362352759       5.47133636       2.13591909
+  ! 0.410784155      5.83882189      6.71128035        1.31730068       1.90963650
+
+  ! single complex exponential random variate with real part of scale=0.5 (lambda=2.0);
+  ! imagainary part of scale=1.6 (lambda=0.625)
   cloc   = (0.0, 0.0)
   cscale = (0.5, 1.6)
   print *, rexp(cloc, cscale)
-!single complex exponential random variate with real part of scale=0.5 (lambda=2.0);
-!imagainary part of scale=1.6 (lambda=0.625)
-
-! (0.219550118,1.01847279)
+  ! (0.426896989,2.56968451)
 
 end program example_exponential_rvs
diff --git a/src/stdlib_stats_distribution_exponential.fypp b/src/stdlib_stats_distribution_exponential.fypp
index ffebb3299..cf4b43ab3 100644
--- a/src/stdlib_stats_distribution_exponential.fypp
+++ b/src/stdlib_stats_distribution_exponential.fypp
@@ -9,7 +9,7 @@ module stdlib_stats_distribution_exponential
     implicit none
     private
 
-    integer :: ke(0:255)
+    integer  :: ke(0:255)
     real(dp) :: we(0:255), fe(0:255)
     logical  :: zig_exp_initialized = .false.
 
@@ -26,14 +26,26 @@ module stdlib_stats_distribution_exponential
     !! ([Specification](../page/specs/stdlib_stats_distribution_exponential.html#
     !! rvs_exp-exponential-distribution-random-variates))
     !!
-        module procedure rvs_exp_0_rsp                 !0 dummy variable
+        module procedure rvs_exp_0_rsp                        !0 dummy variable
+
+        ! new interfaces using loc and scale
+
+        #:for k1, t1 in RC_KINDS_TYPES
+        module procedure rvs_exp_${t1[0]}$${k1}$              !1 dummy variable
+        #:endfor
+
+        #:for k1, t1 in RC_KINDS_TYPES
+        module procedure rvs_exp_array_${t1[0]}$${k1}$        !2 dummy variables
+        #:endfor
+
+        ! original interfaces using lambda
 
         #:for k1, t1 in RC_KINDS_TYPES
-        module procedure rvs_exp_${t1[0]}$${k1}$       !1 dummy variable
+        module procedure rvs_exp_lambda_${t1[0]}$${k1}$       !1 dummy variable
         #:endfor
 
         #:for k1, t1 in RC_KINDS_TYPES
-        module procedure rvs_exp_array_${t1[0]}$${k1}$ !2 dummy variables
+        module procedure rvs_exp_array_lambda_${t1[0]}$${k1}$ !2 dummy variables
         #:endfor
     end interface rvs_exp
 
@@ -46,9 +58,17 @@ module stdlib_stats_distribution_exponential
     !! ([Specification](../page/specs/stdlib_stats_distribution_exponential.html#
     !! pdf_exp-exponential-distribution-probability-density-function))
     !!
+        ! new interfaces using loc and scale
+
         #:for k1, t1 in RC_KINDS_TYPES
         module procedure pdf_exp_${t1[0]}$${k1}$
         #:endfor
+
+        ! original interfaces using lambda
+
+        #:for k1, t1 in RC_KINDS_TYPES
+        module procedure pdf_exp_lambda_${t1[0]}$${k1}$
+        #:endfor
     end interface pdf_exp
 
 
@@ -60,9 +80,17 @@ module stdlib_stats_distribution_exponential
     !! ([Specification](../page/specs/stdlib_stats_distribution_exponential.html#
     !! cdf_exp-exponential-distribution-cumulative-distribution-function))
     !!
+        ! new interfaces using loc and scale
+
         #:for k1, t1 in RC_KINDS_TYPES
         module procedure cdf_exp_${t1[0]}$${k1}$
         #:endfor
+
+        ! original interfaces using lambda
+
+        #:for k1, t1 in RC_KINDS_TYPES
+        module procedure cdf_exp_lambda_${t1[0]}$${k1}$
+        #:endfor
     end interface cdf_exp
 
 
@@ -306,7 +334,7 @@ contains
         else if (x < loc) then
             res = 0._${k1}$
         else
-            res = 1.0_sp - exp(- (x - loc) / scale)
+            res = 1.0_${k1}$ - exp(- (x - loc) / scale)
         end if
     end function cdf_exp_${t1[0]}$${k1}$
 
@@ -326,4 +354,137 @@ contains
 
     #:endfor
 
+
+
+
+    !
+    ! below: wrapper functions for interfaces using lambda (for backward compatibility)
+    !
+
+
+
+
+    #:for k1, t1 in REAL_KINDS_TYPES
+    impure elemental function rvs_exp_lambda_${t1[0]}$${k1}$(lambda) result(res)
+    !
+    ! Exponential distributed random variate
+    !
+        ${t1}$, intent(in) :: lambda
+        ${t1}$ :: res
+
+        res = rvs_exp_${t1[0]}$${k1}$(0._${k1}$, 1.0_${k1}$/lambda)
+    end function rvs_exp_lambda_${t1[0]}$${k1}$
+
+    #:endfor
+
+
+
+
+    #:for k1, t1 in CMPLX_KINDS_TYPES
+    impure elemental function rvs_exp_lambda_${t1[0]}$${k1}$(lambda) result(res)
+        ${t1}$, intent(in) :: lambda
+        ${t1}$ :: res
+        real(${k1}$) :: tr, ti
+
+        tr = rvs_exp_r${k1}$(0._${k1}$, 1.0_${k1}$/lambda%re)
+        ti = rvs_exp_r${k1}$(0._${k1}$, 1.0_${k1}$/lambda%im)
+        res = cmplx(tr, ti, kind=${k1}$)
+    end function rvs_exp_lambda_${t1[0]}$${k1}$
+
+    #:endfor
+
+
+
+
+    #:for k1, t1 in REAL_KINDS_TYPES
+    impure function rvs_exp_array_lambda_${t1[0]}$${k1}$(lambda, array_size) result(res)
+        ${t1}$, intent(in) :: lambda
+        integer, intent(in) :: array_size
+        ${t1}$ :: res(array_size)
+
+        res = rvs_exp_array_${t1[0]}$${k1}$(0._${k1}$, 1.0_${k1}$/lambda, array_size)
+    end function rvs_exp_array_lambda_${t1[0]}$${k1}$
+
+    #:endfor
+
+
+
+
+    #:for k1, t1 in CMPLX_KINDS_TYPES
+    impure function rvs_exp_array_lambda_${t1[0]}$${k1}$(lambda, array_size) result(res)
+        ${t1}$, intent(in) :: lambda
+        integer, intent(in) :: array_size
+        ${t1}$ :: res(array_size)
+        integer :: i
+        real(${k1}$) :: tr, ti
+
+        do i = 1, array_size
+            tr = rvs_exp_r${k1}$(0._${k1}$, 1.0_${k1}$/lambda%re)
+            ti = rvs_exp_r${k1}$(0._${k1}$, 1.0_${k1}$/lambda%im)
+            res(i) = cmplx(tr, ti, kind=${k1}$)
+        end do
+    end function rvs_exp_array_lambda_${t1[0]}$${k1}$
+
+    #:endfor
+
+
+
+
+    #:for k1, t1 in REAL_KINDS_TYPES
+    elemental function pdf_exp_lambda_${t1[0]}$${k1}$(x, lambda) result(res)
+    !
+    ! Exponential Distribution Probability Density Function
+    !
+        ${t1}$, intent(in) :: x, lambda
+        real(${k1}$) :: res
+
+        res = pdf_exp_${t1[0]}$${k1}$(x, 0._${k1}$, 1.0_${k1}$/lambda)
+    end function pdf_exp_lambda_${t1[0]}$${k1}$
+
+    #:endfor
+
+
+
+
+    #:for k1, t1 in CMPLX_KINDS_TYPES
+    elemental function pdf_exp_lambda_${t1[0]}$${k1}$(x, lambda) result(res)
+        ${t1}$, intent(in) :: x, lambda
+        real(${k1}$) :: res
+
+        res = pdf_exp_r${k1}$(x%re, 0._${k1}$, 1.0_${k1}$/lambda%re)
+        res = res * pdf_exp_r${k1}$(x%im, 0._${k1}$, 1.0_${k1}$/lambda%im)
+    end function pdf_exp_lambda_${t1[0]}$${k1}$
+
+    #:endfor
+
+
+
+
+    #:for k1, t1 in REAL_KINDS_TYPES
+    elemental function cdf_exp_lambda_${t1[0]}$${k1}$(x, lambda) result(res)
+    !
+    ! Exponential Distribution Cumulative Distribution Function
+    !
+        ${t1}$, intent(in) :: x, lambda
+        real(${k1}$) :: res
+
+        res = cdf_exp_${t1[0]}$${k1}$(x, 0._${k1}$, 1.0_${k1}$/lambda)
+    end function cdf_exp_lambda_${t1[0]}$${k1}$
+
+    #:endfor
+
+
+
+
+    #:for k1, t1 in CMPLX_KINDS_TYPES
+    elemental function cdf_exp_lambda_${t1[0]}$${k1}$(x, lambda) result(res)
+        ${t1}$, intent(in) :: x, lambda
+        real(${k1}$) :: res
+
+        res = cdf_exp_r${k1}$(x%re, 0._${k1}$, 1.0_${k1}$/lambda%re)
+        res = res * cdf_exp_r${k1}$(x%im, 0._${k1}$, 1.0_${k1}$/lambda%im)
+    end function cdf_exp_lambda_${t1[0]}$${k1}$
+
+    #:endfor
+
 end module stdlib_stats_distribution_exponential
diff --git a/test/stats/test_distribution_exponential.fypp b/test/stats/test_distribution_exponential.fypp
index 5df3b29fb..832df2c20 100644
--- a/test/stats/test_distribution_exponential.fypp
+++ b/test/stats/test_distribution_exponential.fypp
@@ -51,6 +51,25 @@ contains
 
         print *, ""
         print *, "Test exponential random generator with chi-squared"
+
+        ! using interface for lambda
+        freq = 0
+        do i = 1, num
+            j = 1000 * (1 - exp(- expon_rvs(1.0)))
+            freq(j) = freq(j) + 1
+        end do
+        chisq = 0.0_dp
+        expct = num / array_size
+        do i = 0, array_size - 1
+           chisq = chisq + (freq(i) - expct) ** 2 / expct
+        end do
+        write(*,*) "The critical values for chi-squared with 1000 d. of f. is" &
+            //" 1143.92"
+        write(*,*) "Chi-squared for exponential random generator is : ", chisq
+        call check((chisq < 1143.9), &
+            msg="exponential randomness failed chi-squared test", warn=warn)
+
+        ! using interface for loc and scale
         freq = 0
         do i = 1, num
             j = 1000 * (1 - exp(- expon_rvs(0.0, 1.0)))
@@ -66,72 +85,86 @@ contains
         write(*,*) "Chi-squared for exponential random generator is : ", chisq
         call check((chisq < 1143.9), &
             msg="exponential randomness failed chi-squared test", warn=warn)
+
     end subroutine test_exponential_random_generator
 
 
 
     #:for k1, t1 in RC_KINDS_TYPES
     subroutine test_expon_rvs_${t1[0]}$${k1}$
-        ${t1}$ :: res(10), loc, scale
+        ${t1}$ :: res(10), lambda, loc, scale
         integer, parameter :: k = 5
         integer :: i
         integer :: seed, get
         #:if t1[0] == "r"
             #! for real type
         ${t1}$, parameter :: ans(10) =                                         &
-                            [ 1.37178108290154243675829093263018876_${k1}$,    &
-                             0.309467303067628429769087006206973456_${k1}$,    &
-                             0.303573393522570872393728791394096334_${k1}$,    &
-                              3.00973636550766943109636031294940040_${k1}$,    &
-                             0.250084097046766984373533659891108982_${k1}$,    &
-                              1.20139122141795795517538181229610927_${k1}$,    &
-                              4.43019214257137261547825346497120336_${k1}$,    &
-                             0.835001950484080046610557701569632627_${k1}$,    &
-                              1.82681711031524329769126779865473509_${k1}$,    &
-                             0.910435173630070204708886194566730410_${k1}$]
+                            [0.609680481289574416337018192280083895_${k1}$,    &
+                             0.137541023585612635452927558314210417_${k1}$,    &
+                             0.134921508232253721063879462841820585_${k1}$,    &
+                              1.33766060689229752493171569464417802_${k1}$,    &
+                             0.111148487576340881943792737729381770_${k1}$,    &
+                             0.533951653963536868966836361020492979_${k1}$,    &
+                              1.96897428558727671799033487332053483_${k1}$,    &
+                             0.371111977992924465160247867364281152_${k1}$,    &
+                             0.811918715695663687862785688290993341_${k1}$,    &
+                             0.404637854946697868759504975362991277_${k1}$]
         #:else
             #! for complex type
         ${t1}$, parameter :: ans(10) =                                         &
-                            [(0.640164505354053137153869101894088070_${k1}$,   &
-                              0.268204995991944639133208738712710328_${k1}$),  &
-                             (0.141667583643866407117073435983911608_${k1}$,   &
-                               2.60843818343998017361684560455614716_${k1}$),  &
-                             (0.116705911955157926040982374615850854_${k1}$,   &
-                               1.04120572522889689448533090398996145_${k1}$),  &
-                              (2.06742299986664055388985161698656149_${k1}$,   &
-                              0.723668357086202707062483341360348315_${k1}$),  &
-                             (0.852514651480446872255924972705542983_${k1}$,   &
-                              0.789043817146060844081034701957833041_${k1}$),  &
-                              (1.09098446025458177821576555288629603_${k1}$,   &
-                               1.48569478096399141264782883808948111_${k1}$),  &
-                              (4.29633077423243321391055360436439499_${k1}$,   &
-                              0.338216396454583145825267820328008412_${k1}$),  &
-                             (0.340462754402863337910289942556119029_${k1}$,   &
-                              0.172319442815022222381671213042864120_${k1}$),  &
-                       (6.932352666201882229746189523211795805E-0002_${k1}$,   &
-                        6.742518436285274002761624956292507704E-0002_${k1}$),  &
-                              (1.03231628501970258415809666985296648_${k1}$,   &
-                              0.421413014732743429480166241773986277_${k1}$)]
+                            [(1.30645817419194517786503898345732266_${k1}$,    &
+                             0.158701181060322271676454874977935106_${k1}$),   &
+                            (0.289117517640543687994027420375329869_${k1}$,    &
+                              1.54345454641418945184428733997405138_${k1}$),   &
+                            (0.238175330520730461308127295134389521_${k1}$,    &
+                             0.616098062265619464192503493485184250_${k1}$),   &
+                             (4.21923061197273582426500329997257485_${k1}$,    &
+                             0.428206128453374382877209077728016710_${k1}$),   &
+                             (1.73982581934785075970596933205212874_${k1}$,    &
+                             0.466889832630805233184044202341912994_${k1}$),   &
+                             (2.22649889847873832288931745486999202_${k1}$,    &
+                             0.879109337848515628785697537331053851_${k1}$),   &
+                             (8.76802198822945553859296653951917464_${k1}$,    &
+                             0.200128045239398311139211728004738688_${k1}$),   &
+                            (0.694821947760945587572020290930855262_${k1}$,    &
+                             0.101964167346166995492113143812345625_${k1}$),   &
+                            (0.141476585024528208770330398432893829_${k1}$,    &
+                       3.989655879458742013468417133900891716E-0002_${k1}$),   &
+                             (2.10676792861163792685325850990401309_${k1}$,    &
+                             0.249356813451327473065187125310051027_${k1}$)]
         #:endif
 
         print *, "Test exponential_distribution_rvs_${t1[0]}$${k1}$"
         seed = 593742186
-        call random_seed(seed, get)
 
+        ! set args
         #:if t1[0] == "r"
             #! for real type
-        loc   = 0.0_${k1}$
-        scale = 1.5_${k1}$
+        lambda = 1.5_${k1}$
+        loc    = 0._${k1}$
+        scale  = 1.0_${k1}$/lambda
         #:else
             #! for complex type
-        loc   = (0.0_${k1}$, 0.0_${k1}$)
-        scale = (0.7_${k1}$, 1.3_${k1}$)
+        lambda = (0.7_${k1}$, 1.3_${k1}$)
+        loc    = (0._${k1}$, 0._${k1}$)
+        scale  = cmplx(1.0_${k1}$/lambda%re, 1.0_${k1}$/lambda%im, kind=${k1}$)
         #:endif
 
+        ! tests using interface for lambda
+        call random_seed(seed, get)
+        do i = 1, k
+            res(i) = expon_rvs(lambda)      ! 1 dummy
+        end do
+        res(6:10) = expon_rvs(lambda, k)    ! 2 dummies
+        call check(all(abs(res - ans) < ${k1}$tol),                            &
+            msg="exponential_distribution_rvs_${t1[0]}$${k1}$ failed", warn=warn)
+
+        ! tests using interface for loc and scale
+        call random_seed(seed, get)
         do i = 1, k
-            res(i) = expon_rvs(loc, scale)      ! 1 dummy
+            res(i) = expon_rvs(loc, scale)
         end do
-        res(6:10) = expon_rvs(loc, scale, k)    ! 2 dummies
+        res(6:10) = expon_rvs(loc, scale, k)
         call check(all(abs(res - ans) < ${k1}$tol),                            &
             msg="exponential_distribution_rvs_${t1[0]}$${k1}$ failed", warn=warn)
     end subroutine test_expon_rvs_${t1[0]}$${k1}$
@@ -144,66 +177,81 @@ contains
     #:for k1, t1 in RC_KINDS_TYPES
     subroutine test_expon_pdf_${t1[0]}$${k1}$
 
-        ${t1}$ :: x1, x2(3,4), loc, scale
+        ${t1}$ :: x1, x2(3,4), lambda, loc, scale
         integer :: seed, get
         real(${k1}$) :: res(3,5)
         #:if t1[0] == "r"
             #! for real type
         real(${k1}$), parameter :: ans(15) =                                   &
-                             [0.161196572913168763707695024965242901_${k1}$,   &
-                              0.161196572913168763707695024965242901_${k1}$,   &
-                              0.161196572913168763707695024965242901_${k1}$,   &
-                              0.643898188440827210152396844674246781_${k1}$,   &
-                              0.483874493503456231093693975081491447_${k1}$,   &
-                         9.03370704401507616746076779036425611E-0002_${k1}$,   &
-                              0.324446322474929270783681833006314743_${k1}$,   &
-                              0.105508812337994867337369061259176307_${k1}$,   &
-                              0.134103192260524265823113451239842656_${k1}$,   &
-                              0.600352329443164063355621930673196730_${k1}$,   &
-                              0.185145886685884149909301423404484569_${k1}$,   &
-                              0.640174124005934997256906214340904849_${k1}$,   &
-                         8.71310352316870081179003238592937984E-0002_${k1}$,   &
-                              0.120610589741161627237827724075984870_${k1}$,   &
-                              0.444928832931631578265476475258011855_${k1}$]
+                             [0.362692289054629718342313806171796533_${k1}$,   &
+                              0.362692289054629718342313806171796533_${k1}$,   &
+                              0.362692289054629718342313806171796533_${k1}$,   &
+                               1.44877092399186122284289290051705535_${k1}$,   &
+                               1.08871761038277651996081144393335589_${k1}$,   &
+                              0.203258408490339213767867275283195750_${k1}$,   &
+                              0.730004225568590859263284124264208147_${k1}$,   &
+                              0.237394827760488451509080387833146683_${k1}$,   &
+                              0.301732182586179598102005265289645959_${k1}$,   &
+                               1.35079274124711914255014934401469271_${k1}$,   &
+                              0.416578245043239337295928202660090263_${k1}$,   &
+                               1.44039177901335374382803898226703593_${k1}$,   &
+                              0.196044829271295768265275728683411055_${k1}$,   &
+                              0.271373826917613661285112379170965958_${k1}$,   &
+                               1.00108987409617105109732206933052664_${k1}$]
         #:else
             #! for complex type
         real(${k1}$), parameter :: ans(15) =                                   &
-                             [0.486535224757776955373552792251950892_${k1}$,   &
-                              0.486535224757776955373552792251950892_${k1}$,   &
-                              0.486535224757776955373552792251950892_${k1}$,   &
-                              0.204899082205378114034570971362956231_${k1}$,   &
-                              0.160462247586374432191047938164570635_${k1}$,   &
-                              0.377386705590797968776822125514642235_${k1}$,   &
-                              0.555588777292678074202874575318307322_${k1}$,   &
-                         4.92605884877423501624127196918217120E-0002_${k1}$,   &
-                               1.27717230149361435509455319481070053_${k1}$,   &
-                              0.202330648081272095897577464423159785_${k1}$,   &
-                              0.123454294230420925843509908198290816_${k1}$,   &
-                              0.702514356837609534474727020137414207_${k1}$,   &
-                              0.183552428976738966628798837688943286_${k1}$,   &
-                              0.764400963035895183003646698336710458_${k1}$,   &
-                              0.465938985248816058528756692077795393_${k1}$]
+                             [0.112097715784191810518066563334849515_${k1}$,   &
+                              0.112097715784191810518066563334849515_${k1}$,   &
+                              0.112097715784191810518066563334849515_${k1}$,   &
+                         4.72087485401191174735651518020251204E-0002_${k1}$,   &
+                         3.69705018439006691768174449531170720E-0002_${k1}$,   &
+                         8.69498969681198520061798177185735738E-0002_${k1}$,   &
+                              0.128007654288233028296342302153338001_${k1}$,   &
+                         1.13496395875758374774198906169957218E-0002_${k1}$,   &
+                              0.294260498264128747413785056084385424_${k1}$,   &
+                         4.66169813179250908948018478030960097E-0002_${k1}$,   &
+                         2.84438693906889813143446828488861951E-0002_${k1}$,   &
+                              0.161859307815385236742977105439660254_${k1}$,   &
+                         4.22904796362406579112752522035325397E-0002_${k1}$,   &
+                              0.176117981883470250164040199296778089_${k1}$,   &
+                              0.107352342201327219885025541854724060_${k1}$]
         #:endif
 
         print *, "Test exponential_distribution_pdf_${t1[0]}$${k1}$"
         seed = 123987654
-        call random_seed(seed, get)
+
+        ! set args
         #:if t1[0] == "r"
             #! for real type
-        loc   = 0.0_${k1}$
-        scale = 1.5_${k1}$
+        lambda = 1.5_${k1}$
+        loc    = 0._${k1}$
+        scale  = 1.0_${k1}$/lambda
         #:else
             #! for complex type
-        loc   = (0.0_${k1}$, 0.0_${k1}$)
-        scale = (0.3_${k1}$, 1.6_${k1}$)
+        lambda = (0.3_${k1}$, 1.6_${k1}$)
+        loc    = (0._${k1}$, 0._${k1}$)
+        scale  = cmplx(1.0_${k1}$/lambda%re, 1.0_${k1}$/lambda%im, kind=${k1}$)
         #:endif
 
+        ! tests using interface for lambda
+        call random_seed(seed, get)
+        x1 = expon_rvs(lambda)
+        x2 = reshape(expon_rvs(lambda, 12), [3,4])
+        res(:,1) = expon_pdf(x1, lambda)
+        res(:, 2:5) = expon_pdf(x2, lambda)
+        call check(all(abs(res - reshape(ans, [3,5])) < ${k1}$tol),            &
+            msg="exponential_distribution_pdf_${t1[0]}$${k1}$ failed", warn=warn)
+
+        ! tests using interface for loc and scale
+        call random_seed(seed, get)
         x1 = expon_rvs(loc, scale)
         x2 = reshape(expon_rvs(loc, scale, 12), [3,4])
         res(:,1) = expon_pdf(x1, loc, scale)
         res(:, 2:5) = expon_pdf(x2, loc, scale)
         call check(all(abs(res - reshape(ans, [3,5])) < ${k1}$tol),            &
             msg="exponential_distribution_pdf_${t1[0]}$${k1}$ failed", warn=warn)
+
     end subroutine test_expon_pdf_${t1[0]}$${k1}$
 
     #:endfor
@@ -214,7 +262,7 @@ contains
     #:for k1, t1 in RC_KINDS_TYPES
     subroutine test_expon_cdf_${t1[0]}$${k1}$
 
-        ${t1}$ :: x1, x2(3,4), loc, scale
+        ${t1}$ :: x1, x2(3,4), lambda, loc, scale
         integer :: seed, get
         real(${k1}$) :: res(3,5)
         #:if t1[0] == "r"
@@ -256,23 +304,37 @@ contains
 
         print *, "Test exponential_distribution_cdf_${t1[0]}$${k1}$"
         seed = 621957438
-        call random_seed(seed, get)
 
+        ! set args
         #:if t1[0] == "r"
             #! for real type
-        loc   = 0.0_${k1}$
-        scale = 2.0_${k1}$
+        lambda = 2.0_${k1}$
+        loc    = 0._${k1}$
+        scale  = 1.0_${k1}$/lambda
         #:else
-        loc   = (0.0_${k1}$, 0.0_${k1}$)
-        scale = (1.3_${k1}$, 2.1_${k1}$)
+        lambda = (1.3_${k1}$, 2.1_${k1}$)
+        loc    = (0._${k1}$, 0._${k1}$)
+        scale  = cmplx(1.0_${k1}$/lambda%re, 1.0_${k1}$/lambda%im, kind=${k1}$)
         #:endif
 
+        ! tests using interface for lambda
+        call random_seed(seed, get)
+        x1 = expon_rvs(lambda)
+        x2 = reshape(expon_rvs(lambda, 12), [3,4])
+        res(:,1) = expon_cdf(x1, lambda)
+        res(:, 2:5) = expon_cdf(x2, lambda)
+        call check(all(abs(res - reshape(ans,[3,5])) < ${k1}$tol),             &
+            msg="exponential_distribution_cdf_${t1[0]}$${k1}$ failed", warn=warn)
+
+        ! tests using interface for loc and scale
+        call random_seed(seed, get)
         x1 = expon_rvs(loc, scale)
         x2 = reshape(expon_rvs(loc, scale, 12), [3,4])
         res(:,1) = expon_cdf(x1, loc, scale)
         res(:, 2:5) = expon_cdf(x2, loc, scale)
         call check(all(abs(res - reshape(ans,[3,5])) < ${k1}$tol),             &
             msg="exponential_distribution_cdf_${t1[0]}$${k1}$ failed", warn=warn)
+
     end subroutine test_expon_cdf_${t1[0]}$${k1}$
 
     #:endfor

From ba239c6a671f9f6da5a48f57119b587155c3add9 Mon Sep 17 00:00:00 2001
From: Sebastian <sebastian@mutz.science>
Date: Tue, 13 May 2025 20:40:03 +0100
Subject: [PATCH 3/7] Trigger mergeability check


From 9fe477b17530ba3e3c0f7d66a791fd886e840dff Mon Sep 17 00:00:00 2001
From: Federico Perini <federico.perini@gmail.com>
Date: Fri, 16 May 2025 18:27:57 +0200
Subject: [PATCH 4/7] Update doc/specs/stdlib_stats_distribution_exponential.md

---
 doc/specs/stdlib_stats_distribution_exponential.md | 5 +----
 1 file changed, 1 insertion(+), 4 deletions(-)

diff --git a/doc/specs/stdlib_stats_distribution_exponential.md b/doc/specs/stdlib_stats_distribution_exponential.md
index 27f5919a4..38177fde6 100644
--- a/doc/specs/stdlib_stats_distribution_exponential.md
+++ b/doc/specs/stdlib_stats_distribution_exponential.md
@@ -116,10 +116,7 @@ All arguments must have the same type.
 
 ### Return value
 
-If `lambda` is passed, the result is a scalar or an array, with a shape conformable to the arguments, and the same type as the input arguments. If `lambda` is non-positive, the result is `NaN`.
-
-
-If `loc` and `scale` are passed, the result is a scalar or an array, with a shape conformable to the arguments, and the same type as the input arguments. If `scale` is non-positive, the result is `NaN`.
+The result is a scalar or an array, with a shape conformable to the arguments, and the same type as the input arguments. If non-positive `lambda` or `scale`, the result is `NaN`.
 
 
 ### Example

From 3c5114bbc07bd18d8c613f361a84bc5489b9a0b4 Mon Sep 17 00:00:00 2001
From: Federico Perini <federico.perini@gmail.com>
Date: Fri, 16 May 2025 18:28:10 +0200
Subject: [PATCH 5/7] Update doc/specs/stdlib_stats_distribution_exponential.md

---
 doc/specs/stdlib_stats_distribution_exponential.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/doc/specs/stdlib_stats_distribution_exponential.md b/doc/specs/stdlib_stats_distribution_exponential.md
index 38177fde6..3390ed7b9 100644
--- a/doc/specs/stdlib_stats_distribution_exponential.md
+++ b/doc/specs/stdlib_stats_distribution_exponential.md
@@ -141,7 +141,7 @@ For a complex variable  \(z=(x + y i)\) with independent real \(x\) and imaginar
 
 $$F(x+\mathit{i}y)=F(x)F(y)=\begin{cases} (1 - e^{-\lambda_{x} x})(1 - e^{-\lambda_{y} y}) &x\geqslant 0, \;\; y\geqslant 0 \\\\ 0 & \text{otherwise} \end{cases}$$
 
-Instead of of the inverse scale parameter `lambda`, it is possible to pass `loc` and `scale`, where \(scale = \frac{1}{\lambda}\) and `loc` specifies the value by which the distribution is shifted.
+Alternative to the inverse scale parameter `lambda`, it is possible to pass `loc` and `scale`, where \(scale = \frac{1}{\lambda}\) and `loc` specifies the value by which the distribution is shifted.
 
 ### Syntax
 

From 3ae8b58b89d2dad816d2e70bcc6e7445137201cd Mon Sep 17 00:00:00 2001
From: Federico Perini <federico.perini@gmail.com>
Date: Fri, 16 May 2025 18:28:40 +0200
Subject: [PATCH 6/7] Update doc/specs/stdlib_stats_distribution_exponential.md

---
 doc/specs/stdlib_stats_distribution_exponential.md | 5 +----
 1 file changed, 1 insertion(+), 4 deletions(-)

diff --git a/doc/specs/stdlib_stats_distribution_exponential.md b/doc/specs/stdlib_stats_distribution_exponential.md
index 3390ed7b9..f5f2e0268 100644
--- a/doc/specs/stdlib_stats_distribution_exponential.md
+++ b/doc/specs/stdlib_stats_distribution_exponential.md
@@ -171,10 +171,7 @@ All arguments must have the same type.
 
 ### Return value
 
-If `lamba` is passed, the result is a scalar or an array, with a shape conformable to the arguments, and the same type as the input arguments. If `lambda` is non-positive, the result is `NaN`.
-
-
-If `loc` and `scale` are passed, the result is a scalar or an array, with a shape conformable to the arguments, and the same type as the input arguments. If `scale` is non-positive, the result is `NaN`.
+The result is a scalar or an array, with a shape conformable to the arguments, and the same type as the input arguments. With non-positive `lambda` or `scale`, the result is `NaN`.
 
 ### Example
 

From 9b99b53cf6747547329056f4555a3480f5d37390 Mon Sep 17 00:00:00 2001
From: Sebastian <sebastian@mutz.science>
Date: Sat, 17 May 2025 21:02:48 +0100
Subject: [PATCH 7/7] new API prioritised

---
 doc/specs/stdlib_stats_distribution_exponential.md   | 12 ++++++------
 .../example_exponential_cdf.f90                      |  8 ++++----
 .../example_exponential_pdf.f90                      |  8 ++++----
 .../example_exponential_rvs.f90                      | 10 +++++-----
 4 files changed, 19 insertions(+), 19 deletions(-)

diff --git a/doc/specs/stdlib_stats_distribution_exponential.md b/doc/specs/stdlib_stats_distribution_exponential.md
index f5f2e0268..3c6577697 100644
--- a/doc/specs/stdlib_stats_distribution_exponential.md
+++ b/doc/specs/stdlib_stats_distribution_exponential.md
@@ -34,11 +34,11 @@ The algorithm used for generating exponential random variates is fundamentally l
 
 ### Syntax
 
-`result = ` [[stdlib_stats_distribution_exponential(module):rvs_exp(interface)]] `([lambda] [[, array_size]])`
+`result = ` [[stdlib_stats_distribution_exponential(module):rvs_exp(interface)]] `([loc, scale] [[, array_size]])`
 
 or
 
-`result = ` [[stdlib_stats_distribution_exponential(module):rvs_exp(interface)]] `([loc, scale] [[, array_size]])`
+`result = ` [[stdlib_stats_distribution_exponential(module):rvs_exp(interface)]] `([lambda] [[, array_size]])`
 
 ### Class
 
@@ -90,11 +90,11 @@ Instead of of the inverse scale parameter `lambda`, it is possible to pass `loc`
 
 ### Syntax
 
-`result = ` [[stdlib_stats_distribution_exponential(module):pdf_exp(interface)]] `(x, lambda)`
+`result = ` [[stdlib_stats_distribution_exponential(module):pdf_exp(interface)]] `(x, loc, scale)`
 
 or
 
-`result = ` [[stdlib_stats_distribution_exponential(module):pdf_exp(interface)]] `(x, loc, scale)`
+`result = ` [[stdlib_stats_distribution_exponential(module):pdf_exp(interface)]] `(x, lambda)`
 
 ### Class
 
@@ -145,11 +145,11 @@ Alternative to the inverse scale parameter `lambda`, it is possible to pass `loc
 
 ### Syntax
 
-`result = ` [[stdlib_stats_distribution_exponential(module):cdf_exp(interface)]] `(x, lambda)`
+`result = ` [[stdlib_stats_distribution_exponential(module):cdf_exp(interface)]] `(x, loc, scale)`
 
 or
 
-`result = ` [[stdlib_stats_distribution_exponential(module):cdf_exp(interface)]] `(x, loc, scale)`
+`result = ` [[stdlib_stats_distribution_exponential(module):cdf_exp(interface)]] `(x, lambda)`
 
 ### Class
 
diff --git a/example/stats_distribution_exponential/example_exponential_cdf.f90 b/example/stats_distribution_exponential/example_exponential_cdf.f90
index e99edaed9..5df68d88d 100644
--- a/example/stats_distribution_exponential/example_exponential_cdf.f90
+++ b/example/stats_distribution_exponential/example_exponential_cdf.f90
@@ -12,14 +12,14 @@ program example_exponential_cdf
   seed_put = 1234567
   call random_seed(seed_put, seed_get)
 
-  ! standard exponential cumulative distribution at x=1.0 with lambda=1.0
-  print *, exp_cdf(1.0, 1.0)
-  ! 0.632120550
-
   ! standard exponential cumulative distribution at x=1.0 with loc=0.0, scale=1.0
   print *, exp_cdf(1.0, 0.0, 1.0)
   ! 0.632120550
 
+  ! standard exponential cumulative distribution at x=1.0 with lambda=1.0
+  print *, exp_cdf(1.0, 1.0)
+  ! 0.632120550
+
   ! cumulative distribution at x=2.0 with lambda=2
   print *, exp_cdf(2.0, 2.0)
   ! 0.981684387
diff --git a/example/stats_distribution_exponential/example_exponential_pdf.f90 b/example/stats_distribution_exponential/example_exponential_pdf.f90
index c8f9aa379..29760e4e7 100644
--- a/example/stats_distribution_exponential/example_exponential_pdf.f90
+++ b/example/stats_distribution_exponential/example_exponential_pdf.f90
@@ -12,14 +12,14 @@ program example_exponential_pdf
   seed_put = 1234567
   call random_seed(seed_put, seed_get)
 
-  ! probability density at x=1.0 with lambda=1.0
-  print *, exp_pdf(1.0, 1.0)
-  ! 0.367879450
-
   ! probability density at x=1.0 with loc=0 and scale=1.0
   print *, exp_pdf(1.0, 0.0, 1.0)
   ! 0.367879450
 
+  ! probability density at x=1.0 with lambda=1.0
+  print *, exp_pdf(1.0, 1.0)
+  ! 0.367879450
+
   ! probability density at x=2.0 with lambda=2.0
   print *, exp_pdf(2.0, 2.0)
   ! 3.66312787E-02
diff --git a/example/stats_distribution_exponential/example_exponential_rvs.f90 b/example/stats_distribution_exponential/example_exponential_rvs.f90
index 65fa84a65..2f6fb04dd 100644
--- a/example/stats_distribution_exponential/example_exponential_rvs.f90
+++ b/example/stats_distribution_exponential/example_exponential_rvs.f90
@@ -9,18 +9,18 @@ program example_exponential_rvs
   seed_put = 1234567
   call random_seed(seed_put, seed_get)
 
- ! single standard exponential random variate
+  ! single standard exponential random variate
   print *, rexp()
   ! 0.358690143
 
-  ! exponential random variate with lambda=2
-   print *, rexp(2.0)
-  ! 0.204114929
-
   ! exponential random variate with loc=0 and scale=0.5 (lambda=2)
   print *, rexp(0.0, 0.5)
   ! 0.122672431
 
+  ! exponential random variate with lambda=2
+   print *, rexp(2.0)
+  ! 0.204114929
+
   ! exponential random variate with loc=0.6 and scale=0.2 (lambda=5)
   print *, rexp(0.6, 0.2)
   ! 0.681645989