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On the ordered partial sums of real random variables
Lajos Takács
Journal:

Journal of Applied Probability / Volume 14 / Issue 1 / March 1977

Published online by Cambridge University Press:

14 July 2016, pp. 75-88

Print publication:

March 1977
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In 1952 Pollaczek discovered a remarkable formula for the Laplace-Stieltjes transforms of the distributions of the ordered partial sums for a sequence of independent and identically distributed real random variables. In this paper Pollaczek's result is proved in a simple way and is extended for a semi-Markov sequence of real random variables.

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On the ordered partial sums of real random variables