On a Functional Equation Occurring in the Limit Theorem for Maxima with Random Indices

Slobodanka Janković
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Slobodanka Janković: Mathematical Institute

A chapter in Mathematical Statistics and Probability Theory, 1987, pp 209-215 from Springer

Abstract: Abstract In the limit theorem for the sequence of maxima of a random number of independent, identically distributed random variables, the limiting probability distribution G is given by $$ G(x) = \int_0^\infty {{{\left( {F(x)} \right)}^y}dA(y),\;A(0) = 0,\,x\varepsilon R} $$ where A and F are probability distributions. Here we investigate some properties that distributions F and A must satisfy, for given G, in order that the above equation holds.

Keywords: Probability Distribution; Limit Theorem; Divided Difference; Random Index; Positive Random Variable (search for similar items in EconPapers)
Date: 1987
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-3963-9_15

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DOI: 10.1007/978-94-009-3963-9_15

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