11-9.cpp

#include <numeric>
#include <cmath>
#include <algorithm>
#include <functional>
#include <vector>
#include <iostream>

using namespace std;

template<int N, class T>
T nthPower(T x) {
  T ret = x;
  for (int i=1; i < N; ++i) {
    ret *= x;
  }
  return ret;
}

template<class T, int N>
struct SumDiffNthPower {
  SumDiffNthPower(T x) : mean_(x) { };
  T operator( )(T sum, T current) {
    return sum + nthPower<N>(current - mean_);
  }
  T mean_;
};

template<class T, int N, class Iter_T>
T nthMoment(Iter_T first, Iter_T last, T mean)  {
  size_t cnt = distance(first, last);
  return accumulate(first, last, T( ), SumDiffNthPower<T, N>(mean)) / cnt;
}

template<class T, class Iter_T>
T computeVariance(Iter_T first, Iter_T last, T mean) {
  return nthMoment<T, 2>(first, last, mean);
}

template<class T, class Iter_T>
T computeStdDev(Iter_T first, Iter_T last, T mean) {
  return sqrt(computeVariance(first, last, mean));
}

template<class T, class Iter_T>
T computeSkew(Iter_T begin, Iter_T end, T mean) {
  T m3 = nthMoment<T, 3>(begin, end, mean);
  T m2 = nthMoment<T, 2>(begin, end, mean);
  return m3 / (m2 * sqrt(m2));
}

template<class T, class Iter_T>
T computeKurtosisExcess(Iter_T begin, Iter_T end, T mean) {
  T m4 = nthMoment<T, 4>(begin, end, mean);
  T m2 = nthMoment<T, 2>(begin, end, mean);
  return m4 / (m2 * m2) - 3;
}

template<class T, class Iter_T>
void computeStats(Iter_T first, Iter_T last, T& sum, T& mean,
  T& var, T& std_dev, T& skew, T& kurt)
{
  size_t cnt = distance(first, last);
  sum = accumulate(first, last, T( ));
  mean = sum / cnt;
  var = computeVariance(first, last, mean);
  std_dev = sqrt(var);
  skew = computeSkew(first, last, mean);
  kurt = computeKurtosisExcess(first, last, mean);
}

int main( )
{
  vector<int> v;
  v.push_back(2);
  v.push_back(4);
  v.push_back(8);
  v.push_back(10);
  v.push_back(99);
  v.push_back(1);
  double sum, mean, var, dev, skew, kurt;
  computeStats(v.begin( ), v.end( ), sum, mean, var, dev, skew, kurt);
  cout << "count = " << v.size( ) << "\n";
  cout << "sum = " << sum << "\n";
  cout << "mean = " << mean << "\n";
  cout << "variance = " << var << "\n";
  cout << "standard deviation = " << dev << "\n";
  cout << "skew = " << skew << "\n";
  cout << "kurtosis excess = " << kurt << "\n";
  cout << endl;
}