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Distributions of the product and ratio of Maxwell and Rayleigh random variables

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Abstract

The distributions of the product and ratio of independent random variables arise in many applied problems. These have been extensively studied by many researchers. In this paper, the distributions of the product | XY | and ratio \(\left| {\frac{X}{Y}} \right|\) have been derived, when X and Y are Maxwell and Rayleigh random variables and are distributed independently of each other. The associated cdfs, pdfs, kth moments, entropies, etc., have been given. To describe the possible shapes of the associated pdfs and entropies, the respective plots are provided. The percentage points associated with the cdfs of the product and ratio have been tabulated.

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Authors and Affiliations

  1. Department of Mathematics, Miami Dade College, Hialeah Campus, Hialeah, FL, 33012, USA

    M. Shakil

  2. Department of Statistics, Florida International University, UniversityPark, Miami, FL, 33199, USA

    B. M. Golam Kibria

  3. Department of Statistics and Information Science, Fu Jen Catholic University, Taipei, Taiwan, ROC

    Kuang-Chao Chang

Authors
  1. M. Shakil
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  2. B. M. Golam Kibria
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  3. Kuang-Chao Chang
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Correspondence to B. M. Golam Kibria.

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Shakil, M., Golam Kibria, B.M. & Chang, KC. Distributions of the product and ratio of Maxwell and Rayleigh random variables. Stat Papers 49, 729–747 (2008). https://doi.org/10.1007/s00362-007-0052-9

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  • DOI: https://doi.org/10.1007/s00362-007-0052-9

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