Exact distribution of the product of $$m$$ gamma and $$n$$ Pareto random variables.(English)Zbl 1216.62021

Summary: Exact expressions are derived for the probability density function (pdf), cumulative distribution function (cdf), shape of the pdf, asymptotics of the pdf and the cdf, Laplace transform, moment properties and the order statistics properties of the product of $$m$$ independent gamma and $$n$$ independent Pareto random variables. Computer programs are provided for computing the probability density function and the associated percentage points. Estimation issues by the methods of moments and maximum likelihood are discussed.

MSC:

 62E15 Exact distribution theory in statistics 33C90 Applications of hypergeometric functions 62G30 Order statistics; empirical distribution functions 62-04 Software, source code, etc. for problems pertaining to statistics
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