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The gamma beta ratio distribution. (English) Zbl 1235.62017

Summary: The important problem of the ratio of gamma and beta distributed random variables is considered. Six motivating applications (from efficiency modeling, income modeling, clinical trials, hydrology, reliability and modeling of infectious diseases) are discussed. Exact expressions are derived for the probability density function, cumulative distribution function, hazard rate function, shape characteristics, moments, factorial moments, variance, skewness, kurtosis, conditional moments, \(L\) moments, characteristic function, mean deviation about the mean, mean deviation about the median, Bonferroni curve, Lorenz curve, percentiles, order statistics and the asymptotic distribution of extreme values. Estimation procedures by the methods of moments and maximum likelihood are provided and their performance is compared by simulations. For maximum likelihood estimation, the Fisher information matrix is derived and the case of censoring is considered. Finally, an application is discussed of the efficiency of warning-time systems.

MSC:

62E15 Exact distribution theory in statistics
62E20 Asymptotic distribution theory in statistics
62F10 Point estimation
33C90 Applications of hypergeometric functions
62G32 Statistics of extreme values; tail inference
65C60 Computational problems in statistics (MSC2010)
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References:

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