Journal of Probability and Statistics (Jan 2020)

Distributions of the Ratio and Product of Two Independent Weibull and Lindley Random Variables

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

DOI
https://doi.org/10.1155/2020/5693129
Journal volume & issue
Vol. 2020

Abstract

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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.