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The product and quotient of general beta distributions

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Abstract

The general beta distribution in 4 parameters, denoted gbeta (α, β; c, d), defined on the interval (c,d) is one of the most useful distributions in statistical applications and in related fields such as Operations Research and Management Science. We give here the exact expressions of the densities of X1X2 and of X1/X2, where X1 and X2 are independent general beta variables, and discuss the relationships between the new results with those already obtained. Applications in Reliability and Bayesian Quality Control are given. A computer program, developed for hypergeometric functions in general, can be used to carry out the precise computation of these densities.

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Authors and Affiliations

  1. Université de Moncton, ElA 3EO, Moncton, NB, Canada

    T. Pham-Gia & N. Turkkan

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  1. T. Pham-Gia
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  2. N. Turkkan
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Additional information

Research supported by NSERC grant A 9249 (Canada). The authors wish to thank Professor François Jacob for several helpful discussions, and an anonymous referee for suggestions that have helped improving the content and the presentation of the paper.

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Pham-Gia, T., Turkkan, N. The product and quotient of general beta distributions. Statistical Papers 43, 537–550 (2002). https://doi.org/10.1007/s00362-002-0122-y

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  • DOI: https://doi.org/10.1007/s00362-002-0122-y

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