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The Correlated Bivariate Noncentral F Distribution and Its Application |
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| Authors: | Shahjahan Khan Budi Pratikno Adriana I. N. Ibrahim |
| Affiliation: | 1. School of Agricultural, Computational and Environmental Sciences, International Centre for Applied Climate Science, University of Southern Queensland, Toowoomba, Australia;2. Department of Mathematics and Natural Science, Jenderal Soedirman University (UNSOED), Indonesia;3. Faculty of Science, Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur, Malaysia |
| Abstract: | This article proposes the singly and doubly correlated bivariate noncentral F (BNCF) distributions. The probability density function (pdf) and the cumulative distribution function (cdf) of the distributions are derived for arbitrary values of the parameters. The pdf and cdf of the distributions for different arbitrary values of the parameters are computed, and their graphs are plotted by writing and implementing new R codes. An application of the correlated BNCF distribution is illustrated in the computations of the power function of the pre-test test for the multivariate simple regression model (MSRM). |
| Keywords: | Bivariate noncentral chi-square distribution Compounding distribution Correlated bivariate noncentral F distribution Noncentrality parameter Power function Pre-test test |