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/* http://www.johndcook.com/blog/skewness_kurtosis/ */ #include "RunningStats.h" #include <cmath> #include <vector> RunningStats::RunningStats() { Clear(); } void RunningStats::Clear() { n = 0; M1 = M2 = M3 = M4 = 0.0; } void RunningStats::Push(double x) { double delta, delta_n, delta_n2, term1; long long n1 = n; n++; delta = x - M1; delta_n = delta / n; delta_n2 = delta_n * delta_n; term1 = delta * delta_n * n1; M1 += delta_n; M4 += term1 * delta_n2 * (n*n - 3*n + 3) + 6 * delta_n2 * M2 - 4 * delta_n * M3; M3 += term1 * delta_n * (n - 2) - 3 * delta_n * M2; M2 += term1; } long long RunningStats::NumDataValues() const { return n; } double RunningStats::Mean() const { return M1; } double RunningStats::Variance() const { return M2/(n-1.0); } double RunningStats::StandardDeviation() const { return sqrt( Variance() ); } double RunningStats::Skewness() const { return sqrt(double(n)) * M3/ pow(M2, 1.5); } double RunningStats::Kurtosis() const { return double(n)*M4 / (M2*M2) - 3.0; } RunningStats operator+(const RunningStats a, const RunningStats b) { RunningStats combined; combined.n = a.n + b.n; double delta = b.M1 - a.M1; double delta2 = delta*delta; double delta3 = delta*delta2; double delta4 = delta2*delta2; combined.M1 = (a.n*a.M1 + b.n*b.M1) / combined.n; combined.M2 = a.M2 + b.M2 + delta2 * a.n * b.n / combined.n; combined.M3 = a.M3 + b.M3 + delta3 * a.n * b.n * (a.n - b.n)/(combined.n*combined.n); combined.M3 += 3.0*delta * (a.n*b.M2 - b.n*a.M2) / combined.n; combined.M4 = a.M4 + b.M4 + delta4*a.n*b.n * (a.n*a.n - a.n*b.n + b.n*b.n) / (combined.n*combined.n*combined.n); combined.M4 += 6.0*delta2 * (a.n*a.n*b.M2 + b.n*b.n*a.M2)/(combined.n*combined.n) + 4.0*delta*(a.n*b.M3 - b.n*a.M3) / combined.n; return combined; } RunningStats& RunningStats::operator+=(const RunningStats& rhs) { RunningStats combined = *this + rhs; *this = combined; return *this; }