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On The Product And Ratio Of Gamma And Weibull Random Variables

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  • Nadarajah, Saralees
  • Kotz, Samuel

Abstract

The distributions of products and ratios of random variables are of interest in many areas of the sciences. In this note, the exact distributions of the product XY and the ratio X/Y are derived when X and Y are gamma and Weibull random variables distributed independently of each other.The authors thank the referee and the editor for carefully reading the paper and for their help in improving the paper.

Suggested Citation

  • Nadarajah, Saralees & Kotz, Samuel, 2006. "On The Product And Ratio Of Gamma And Weibull Random Variables," Econometric Theory, Cambridge University Press, vol. 22(2), pages 338-344, April.
    • Handle: RePEc:cup:etheor:v:22:y:2006:i:02:p:338-344_06
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    Cited by:

    1. Denys Pommeret & Laurence Reboul, 2019. "Approximating the Probability Density Function of a Transformation of Random Variables," Methodology and Computing in Applied Probability, Springer, vol. 21(2), pages 633-645, June.
    2. Mathai, A.M. & Provost, Serge B., 2013. "Generalized Boltzmann factors induced by Weibull-type distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 545-551.
    3. Saralees Nadarajah, 2012. "Exact Distribution of the Product of N Student’s t RVs," Methodology and Computing in Applied Probability, Springer, vol. 14(4), pages 997-1009, December.
    4. Sel Ly & Kim-Hung Pho & Sal Ly & Wing-Keung Wong, 2019. "Determining Distribution for the Quotients of Dependent and Independent Random Variables by Using Copulas," JRFM, MDPI, vol. 12(1), pages 1-27, March.
    5. Frantisek Duris & Juraj Gazdarica & Iveta Gazdaricova & Lucia Strieskova & Jaroslav Budis & Jan Turna & Tomas Szemes, 2018. "Mean and variance of ratios of proportions from categories of a multinomial distribution," Journal of Statistical Distributions and Applications, Springer, vol. 5(1), pages 1-20, December.
    6. Julia Adamska & Łukasz Bielak & Joanna Janczura & Agnieszka Wyłomańska, 2022. "From Multi- to Univariate: A Product Random Variable with an Application to Electricity Market Transactions: Pareto and Student’s t -Distribution Case," Mathematics, MDPI, vol. 10(18), pages 1-29, September.

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