Synopsis

#include <boost/math/statistics/bivariate_statistics.hpp>

namespace boost{ namespace math{ namespace statistics {

    template<class Container>
    auto covariance(Container const & u, Container const & v);

    template<class Container>
    auto means_and_covariance(Container const & u, Container const & v);

    template<class Container>
    auto correlation_coefficient(Container const & u, Container const & v);

}}}

Description

This file provides functions for computing bivariate statistics.

Covariance

Computes the population covariance of two datasets:

std::vector<double> u{1,2,3,4,5};
std::vector<double> v{1,2,3,4,5};
double cov_uv = boost::math::statistics::covariance(u, v);

The implementation follows Bennet et al. The data is not modified. Requires a random-access container. Works with real-valued inputs and does not work with complex-valued inputs.

The algorithm used herein simultaneously generates the mean values of the input data u and v. For certain applications, it might be useful to get them in a single pass through the data. As such, we provide means_and_covariance:

std::vector<double> u{1,2,3,4,5};
std::vector<double> v{1,2,3,4,5};
auto [mu_u, mu_v, cov_uv] = boost::math::statistics::means_and_covariance(u, v);

Correlation Coefficient

Computes the Pearson correlation coefficient of two datasets u and v:

std::vector<double> u{1,2,3,4,5};
std::vector<double> v{1,2,3,4,5};
double rho_uv = boost::math::statistics::correlation_coefficient(u, v);
// rho_uv = 1.

The data must be random access and cannot be complex.

If one or both of the datasets is constant, the correlation coefficient is an indeterminant form (0/0) and definitions must be introduced to assign it a value. We use the following: If both datasets are constant, then the correlation coefficient is 1. If one dataset is constant, and the other is not, then the correlation coefficient is zero.

References