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Duals of multiplicative relationships involving beta and gamma random variables

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  • Jones, M.C.

Abstract

By interpreting four known multiplicative relationships involving independent beta and gamma random variables as scale mixtures, their ‘dual’ mixture relationships are obtained, making links to a variety of other distributional relationships. One consequence of these dual relationships is the provision of a number of first-order Markov processes with beta and gamma marginals.

Suggested Citation

  • Jones, M.C., 2022. "Duals of multiplicative relationships involving beta and gamma random variables," Statistics & Probability Letters, Elsevier, vol. 191(C).
    • Handle: RePEc:eee:stapro:v:191:y:2022:i:c:s0167715222001821
    DOI: 10.1016/j.spl.2022.109668
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    References listed on IDEAS

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    1. Jones, M.C. & Balakrishnan, N., 2021. "Simple functions of independent beta random variables that follow beta distributions," Statistics & Probability Letters, Elsevier, vol. 170(C).
    2. Papadatos, N., 1995. "Intermediate order statistics with applications to nonparametric estimation," Statistics & Probability Letters, Elsevier, vol. 22(3), pages 231-238, February.
    3. Saralees Nadarajah, 2005. "Reliability for some bivariate beta distributions," Mathematical Problems in Engineering, Hindawi, vol. 2005, pages 1-11, January.
    4. Ed McKenzie, 1985. "An Autoregressive Process for Beta Random Variables," Management Science, INFORMS, vol. 31(8), pages 988-997, August.
    5. Saralees Nadarajah, 2009. "A bivariate distribution with gamma and beta marginals with application to drought data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(3), pages 277-301.
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