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Sums, products and ratios of generalized beta variables

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Abstract

Recent papers by Professor T. Pham-Gia derived distributions of sums, products and ratios of independent beta random variables. In this paper, we extend professor Pham-Gia's results when X 1 and X 2 are independent random variables distributed according to two generalized beta distributions. For each of these distributions, we derive exact expressions for the densities of S=X 1+X 2, D=X 1−X 2, P=X 1 X 2, and R=X 2/X 1. The expressions turn out to involve the incomplete beta function as well as the hypergeometric functions of one and two variables.

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  1. Department of Statistics, University of Nebraska, 68583, Lincoln, NE, USA

    Saralees Nadarajah

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  1. Saralees Nadarajah
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Nadarajah, S. Sums, products and ratios of generalized beta variables. Statistical Papers 47, 69–90 (2006). https://doi.org/10.1007/s00362-005-0273-8

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  • DOI: https://doi.org/10.1007/s00362-005-0273-8

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