On the minimum of independent geometrically distributed random variables

Gianfranco Ciardo, Lawrence M. Leemis and David Nicol

Statistics & Probability Letters, 1995, vol. 23, issue 4, 313-326

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.

Keywords: Geometric; distribution; Exponential; distribution; Stochastic; ordering; Order; statistics (search for similar items in EconPapers)
Date: 1995
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Citations: View citations in EconPapers (2)

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