Krzysztof Podgórski

Professor, Prefekt Statistiska institutionen

Certain bivariate distributions and random processes connected with maxima and minima

Författare

Tomasz J. Kozubowski
Krzysztof Podgórski

Summary, in English

The minimum and the maximum of t independent, identically distributed random variables have (Formula presented.) and F^t for their survival (minimum) and the distribution (maximum) functions, where (Formula presented.) and F are their common survival and distribution functions, respectively. We provide stochastic interpretation for these survival and distribution functions for the case when t > 0 is no longer an integer. A new bivariate model with these margins involve maxima and minima with a random number of terms. Our construction leads to a bivariate max-min process with t as its time argument. The second coordinate of the process resembles the well-known extremal process and shares with it the one-dimensional distribution given by F^t. However, it is shown that the two processes are different. Some fundamental properties of the max-min process are presented, including a distributional Markovian characterization of its jumps and their locations.

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