Calculate mean and standard deviation from a vector of samples in C++ using Boost

Question

Is there a way to calculate mean and standard deviation for a vector containing samples using Boost?

Or do I have to create an accumulator and feed the vector into it?

Answer 1

I don't know if Boost has more specific functions, but you can do it with the standard library.

Given std::vector<double> v, this is the naive way:

#include <numeric>

double sum = std::accumulate(v.begin(), v.end(), 0.0);
double mean = sum / v.size();

double sq_sum = std::inner_product(v.begin(), v.end(), v.begin(), 0.0);
double stdev = std::sqrt(sq_sum / v.size() - mean * mean);

This is susceptible to overflow or underflow for huge or tiny values. A slightly better way to calculate the standard deviation is:

double sum = std::accumulate(v.begin(), v.end(), 0.0);
double mean = sum / v.size();

std::vector<double> diff(v.size());
std::transform(v.begin(), v.end(), diff.begin(),
               std::bind2nd(std::minus<double>(), mean));
double sq_sum = std::inner_product(diff.begin(), diff.end(), diff.begin(), 0.0);
double stdev = std::sqrt(sq_sum / v.size());

UPDATE for C++11:

The call to std::transform can be written using a lambda function instead of std::minus and std::bind2nd(now deprecated):

std::transform(v.begin(), v.end(), diff.begin(), [mean](double x) { return x - mean; });