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- [/
- Copyright 2018 Nick Thompson
- Distributed under the Boost Software License, Version 1.0.
- (See accompanying file LICENSE_1_0.txt or copy at
- http://www.boost.org/LICENSE_1_0.txt).
- ]
- [section:bivariate_statistics Bivariate Statistics]
- [heading 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);
- }}}
- ``
- [heading Description]
- This file provides functions for computing bivariate statistics.
- [heading 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 [@https://doi.org/10.1109/CLUSTR.2009.5289161 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);
- [heading Correlation Coefficient]
- Computes the [@https://en.wikipedia.org/wiki/Pearson_correlation_coefficient 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.
- [heading References]
- * Bennett, Janine, et al. ['Numerically stable, single-pass, parallel statistics algorithms.] Cluster Computing and Workshops, 2009. CLUSTER'09. IEEE International Conference on. IEEE, 2009.
- [endsect]
- [/section:bivariate_statistics Bivariate Statistics]
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