2 Copyright 2018 Nick Thompson
4 Distributed under the Boost Software License, Version 1.0.
5 (See accompanying file LICENSE_1_0.txt or copy at
6 http://www.boost.org/LICENSE_1_0.txt).
9 [section:bivariate_statistics Bivariate Statistics]
14 #include <boost/math/statistics/bivariate_statistics.hpp>
16 namespace boost{ namespace math{ namespace statistics {
18 template<class Container>
19 auto covariance(Container const & u, Container const & v);
21 template<class Container>
22 auto means_and_covariance(Container const & u, Container const & v);
24 template<class Container>
25 auto correlation_coefficient(Container const & u, Container const & v);
32 This file provides functions for computing bivariate statistics.
36 Computes the population covariance of two datasets:
38 std::vector<double> u{1,2,3,4,5};
39 std::vector<double> v{1,2,3,4,5};
40 double cov_uv = boost::math::statistics::covariance(u, v);
42 The implementation follows [@https://doi.org/10.1109/CLUSTR.2009.5289161 Bennet et al].
43 The data is not modified. Requires a random-access container.
44 Works with real-valued inputs and does not work with complex-valued inputs.
46 The algorithm used herein simultaneously generates the mean values of the input data /u/ and /v/.
47 For certain applications, it might be useful to get them in a single pass through the data.
48 As such, we provide `means_and_covariance`:
50 std::vector<double> u{1,2,3,4,5};
51 std::vector<double> v{1,2,3,4,5};
52 auto [mu_u, mu_v, cov_uv] = boost::math::statistics::means_and_covariance(u, v);
54 [heading Correlation Coefficient]
56 Computes the [@https://en.wikipedia.org/wiki/Pearson_correlation_coefficient Pearson correlation coefficient] of two datasets /u/ and /v/:
58 std::vector<double> u{1,2,3,4,5};
59 std::vector<double> v{1,2,3,4,5};
60 double rho_uv = boost::math::statistics::correlation_coefficient(u, v);
63 The data must be random access and cannot be complex.
65 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.
66 We use the following: If both datasets are constant, then the correlation coefficient is 1.
67 If one dataset is constant, and the other is not, then the correlation coefficient is zero.
72 * Bennett, Janine, et al. ['Numerically stable, single-pass, parallel statistics algorithms.] Cluster Computing and Workshops, 2009. CLUSTER'09. IEEE International Conference on. IEEE, 2009.
75 [/section:bivariate_statistics Bivariate Statistics]