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Hassan, N. J.; Nasar, A. Hawad; Hadad, J. Mahdi

Distributions of the ratio and product of two independent Weibull and Lindley random variables. (English) Zbl 1440.62061

J. Probab. Stat. 2020, Article ID 5693129, 8 p. (2020).
Summary: In this paper, we derive the cumulative distribution functions (CDF) and probability density functions (PDF) of the ratio and product of two independent Weibull and Lindley random variables. The moment generating functions (MGF) and the \(k\)-moment are driven from the ratio and product cases. In these derivations, we use some special functions, for instance, generalized hypergeometric functions, confluent hypergeometric functions, and the parabolic cylinder functions. Finally, we draw the PDF and CDF in many values of the parameters.

MSC:

62E15 Exact distribution theory in statistics
62N05 Reliability and life testing
60E05 Probability distributions: general theory
33C15 Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\)

Keywords:

distributions; ratio and product of two independent Weibull random variables; ratio and product of two independent Lindley random variables
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References:

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