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On the minimum of independent geometrically distributed random variables

Ciardo, Gianfranco
; 
Leemis, Lawrence
; 
Nicol, David
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.
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Date
1995
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Elsevier
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Computational & Applied Mathematics & Statistics
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Computational & Applied Mathematics & Statistics
DOI
https://doi.org/10.1016/0167-7152(94)00130-Z
URI
https://scholarworks.wm.edu/handle/internal/1049
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