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

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

Abstract

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.

Suggested Citation

  • N. J. Hassan & A. Hawad Nasar & J. Mahdi Hadad, 2020. "Distributions of the Ratio and Product of Two Independent Weibull and Lindley Random Variables," Journal of Probability and Statistics, Hindawi, vol. 2020, pages 1-8, May.
    • Handle: RePEc:hin:jnljps:5693129
    DOI: 10.1155/2020/5693129
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