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Biometrika 1977 64(1):167-169; doi:10.1093/biomet/64.1.167
© 1977 by Biometrika Trust
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Miscellanea

Some representations of stable random variables as products

E. J. WILLIAMS

Department of Statistics, University of Melbourne parkville, Victoria

If X{alpha} is a positive stable random variable whose characteristic exonent {alpha} is the reciprocal of an integer n, then X{alpha}–1 is distributed as the product of n–1 mutually independent gamma random variables with parameters {alpha}, 2{alpha}, ..., 1–{alpha}. The results are derived by elementary means from known facts about stable distributions.

Key Words: Gamma distribution • Products • Stable distribution


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