Enhancement: Addition of Probability Functions

src/index.ts

@@ -14,3 +14,4 @@ export * as Random from './random';
 export * as Regression from './regression';
 export * from './statistics';
 export * from './vector';
+export * from './probability';

src/probability.ts

@@ -0,0 +1,90 @@
+// Probability Library
+
+import { factorial } from "./combinatorics";
+
+// Factorial function
+
+  // Combinations function
+  export function combinations(n: number, r: number): number {
+    if (n < 0 || r < 0 || n < r || !Number.isInteger(n) || !Number.isInteger(r)) {
+      throw new Error('Invalid input for combinations.');
+    }
+    return factorial(n) / (factorial(r) * factorial(n - r));
+  }
+
+  // Probability Mass Function (PMF) for a discrete random variable
+  export function pmf(x: number, p: number): number {
+    // Assuming x is a non-negative integer
+    if (x < 0 || !Number.isInteger(x)) {
+      throw new Error('PMF is only defined for non-negative integers.');
+    }
+    return Math.pow(1 - p, x - 1) * p;
+  }
+
+  // Cumulative Distribution Function (CDF) for a discrete random variable
+  export function cdf(x: number, p: number): number {
+    // Assuming x is a non-negative integer
+    if (x < 0 || !Number.isInteger(x)) {
+      throw new Error('CDF is only defined for non-negative integers.');
+    }
+    return 1 - Math.pow(1 - p, x);
+  }
+
+  // Binomial Distribution Probability
+  export function binomialProbability(x: number, n: number, p: number): number {
+    // Assuming x is a non-negative integer
+    if (x < 0 || !Number.isInteger(x)) {
+      throw new Error('Binomial distribution is only defined for non-negative integers.');
+    }
+    return combinations(n, x) * Math.pow(p, x) * Math.pow(1 - p, n - x);
+  }
+
+  // Geometric Distribution Probability
+  export function geometricProbability(x: number, p: number): number {
+    // Assuming x is a non-negative integer
+    if (x < 0 || !Number.isInteger(x)) {
+      throw new Error('Geometric distribution is only defined for non-negative integers.');
+    }
+    return Math.pow(1 - p, x - 1) * p;
+  }
+
+  // Poisson Distribution Probability
+  export function poissonProbability(x: number, λ: number): number {
+    // Assuming x is a non-negative integer
+    if (x < 0 || !Number.isInteger(x)) {
+      throw new Error('Poisson distribution is only defined for non-negative integers.');
+    }
+    return Math.exp(-λ) * Math.pow(λ, x) / factorial(x);
+  }
+
+  // Normal Distribution Probability
+  export function normalProbability(x: number, mean: number, stdDev: number): number {
+    return (1 / (stdDev * Math.sqrt(2 * Math.PI))) * Math.exp(-0.5 * Math.pow((x - mean) / stdDev, 2));
+  }
+
+  // Exponential Distribution Probability
+  export function exponentialProbability(x: number, λ: number): number {
+    return λ * Math.exp(-λ * x);
+  }
+
+  // Uniform Distribution Probability
+  export function uniformProbability(x: number, a: number, b: number): number {
+    if (x >= a && x <= b) {
+      return 1 / (b - a);
+    }
+    return 0;
+  }
+
+  // Joint Probability of two independent events
+  export function jointProbability(eventA: number, eventB: number): number {
+    return eventA * eventB;
+  }
+
+  // Conditional Probability of event A given that event B has occurred
+  export function conditionalProbability(eventA: number, eventB: number): number {
+    if (eventB === 0) {
+      throw new Error('Cannot calculate conditional probability when eventB has zero probability.');
+    }
+    return eventA / eventB;
+  }
+