Product Moments of Sample Variances and Correlation for Variables with Bivariate Normal Distribution
- 1 Center for Research and Teaching in Economics (CIDE), Mexico
Abstract
A general result to obtain the product moments of two sample variances and the sample correlation when the data follow a bivariate normal distribution is derived; the result is expressed in terms of the hypergeometric function. As corollaries, two general equations are stated, one to obtain the moments of the correlation sample and one to obtain the moments of the ratio of two sample variances. To evaluate the product moments in short closed forms, three theorems have been established. The results are used to obtain the expectation and variance for the ratio of two correlated sample variances. Finally, some examples of particular product moments are provided and some validations were carried out.
DOI: https://doi.org/10.3844/jmssp.2016.12.22
Copyright: © 2016 Juan Romero-Padilla. This is an open access article distributed under the terms of the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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Keywords
- Wishart Distribution
- Product Moments
- Hypergeometric Function
- Sample Correlation Coefficient
- Sample Variance