On the minimum of independent geometrically distributed random variables

Authors

Gianfranco Ciardo
Lawrence Leemis, William & MaryFollow
David Nicol

Document Type

Article

Department/Program

Computational & Applied Mathematics & Statistics

Journal Title

Statistics and Probability Letters

Pub Date

1995

Publisher

Elsevier

Volume

23

Issue

4

First Page

313

Abstract

The expectations E[X(1)], E[Z(1)], and E[Y(1)] of the minimum of n independent geometric, modified geometric, or exponential random variables with matching expectations differ. We show how this is accounted for by stochastic variability and how E[X(1)]/E[Y(1)] equals the expected number of ties at the minimum for the geometric random variables. We then introduce the “shifted geometric distribution”, and show that there is a unique value of the shift for which the individual shifted geometric and exponential random variables match expectations both individually and in their minimums.

Recommended Citation

Ciardo, Gianfranco; Leemis, Lawrence; and Nicol, David, On the minimum of independent geometrically distributed random variables (1995). Statistics and Probability Letters, 23(4), 313-326.
https://doi.org/10.1016/0167-7152(94)00130-Z

DOI

https://doi.org/10.1016/0167-7152(94)00130-Z

Publisher Statement

This version is the accepted (post-print) version of the manuscript.