On the maximum and minimum of multivariate Pareto random variables

Abstract

Aksomaitis and Burauskaite-Harju [Information Technology and Control, 38, 2009, 301-302] studied the distribution of $\max (X_1, X_2, \ldots, X_p)$ when $(X_1, X_2, \ldots, X_p)$ follows the multivariate normal distribution.  Here, we study the distributions of $\min (X_1, X_2, \ldots, X_p)$ and $\max (X_1$, $X_2$, $\ldots$, $X_p)$ when $(X_1$, $X_2$, $\ldots$, $X_p)$ follows the most commonly known multivariate Pareto distribution.  Multivariate Pareto distributions are most relevant for modeling extreme values.

DOI: http://dx.doi.org/10.5755/j01.itc.42.3.2148