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

A.G. Pakes

Statistica Neerlandica, 1992, vol. 46, issue 2‐3, 209-218

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.

Date: 1992
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