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On The Minimum Of Independent Geometrically Distributed Random Variables, Gianfranco Ciardo, Lawrence Leemis, David Nicol
On The Minimum Of Independent Geometrically Distributed Random Variables, Gianfranco Ciardo, Lawrence Leemis, David Nicol
Arts & Sciences Articles
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 …