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A characterization of gamma mixtures of stable laws motivated by limit theorems

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  • A.G. Pakes

Abstract

This pape; is concerned with distributional solutions of X1+…+ Xmd= U(X1+…+ Xm+n) where the X's are iid and independent of U which takes values in [0,1]. When U is a constant the only possible non‐trivial solutions lie in the class of semi‐stable laws, and they are stable under a simple regularity condition. This material is reviewed. A unified account is given of some results known for the case where U has a beta (α, 1) law, apparently the only other case allowing explicit identification of all possible solutions.

Suggested Citation

  • A.G. Pakes, 1992. "A characterization of gamma mixtures of stable laws motivated by limit theorems," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 46(2‐3), pages 209-218, July.
    • Handle: RePEc:bla:stanee:v:46:y:1992:i:2-3:p:209-218
    DOI: 10.1111/j.1467-9574.1992.tb01338.x
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    Cited by:

    1. Pakes, Anthony G., 1995. "Characterization of discrete laws via mixed sums and Markov branching processes," Stochastic Processes and their Applications, Elsevier, vol. 55(2), pages 285-300, February.
    2. Yury Khokhlov & Victor Korolev & Alexander Zeifman, 2020. "Multivariate Scale-Mixed Stable Distributions and Related Limit Theorems," Mathematics, MDPI, vol. 8(5), pages 1-29, May.

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