On the Quotient of Extreme Order Statistics from Two Triangularly Distributed Random Variables

Abstract

Abstract Although computer simulations can be used in computations of various characteristics of a stochastic problem to get an approximate answer, we frequently require exact results. When the uncertainty of this problem is restricted within some bounded domain, a triangular distribution may be used appropriately for modeling. In this work, we consider two triangularly and independently distributed random variables. We derive the exact distribution of the ratio of the maximum of these random variables to their minimum. This ratio of extreme statistics may be used as a dispersion measure. We present the quotient distribution in a computable form. Two possible applications are also given.