On the Minimum of Independent Geometrically Distributed Random Variables
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 iii their minimums. Geometric distribution, Exponential distribution, Stochastic ordering, Order statistics
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1994
- Accession Number
- ADA279629
Entities
People
- David Nicol
- Gianfranco Ciardo
- Lawrence M. Leemis