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Products of double gamma, gamma and beta distributions

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  • Chamayou, J.-F.Jean-François

Abstract

This paper considers the double gamma distribution on the real line [lambda]c with Laplace transform (1-t2)-c and the distributions of the products of independent random variables X,Y1,...,Yp,U1,...,Uq, where X is double gamma, the Y's are gamma and the U's are beta. These distributions are typical of what are called lambda distributions. Although they are obtained by multiplicative convolution, these lambda distributions are shown to be distributions occurring with additive convolution. This phenomena appears in a non-trivial way, specially when the Bailey's reduction formulas for hypergeometric functions are used.

Suggested Citation

  • Chamayou, J.-F.Jean-François, 2004. "Products of double gamma, gamma and beta distributions," Statistics & Probability Letters, Elsevier, vol. 68(2), pages 199-208, June.
    • Handle: RePEc:eee:stapro:v:68:y:2004:i:2:p:199-208
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    References listed on IDEAS

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    1. Wise, Gary L. & Hall, Eric B., 1991. "A note on the distribution of the determinant of a random matrix," Statistics & Probability Letters, Elsevier, vol. 11(2), pages 147-148, February.
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    Cited by:

    1. Zhang, Zhehao, 2019. "On the stochastic equation L(Z)=L[V(X+Z)] and properties of Mittag–Leffler distributions," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 365-376.

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