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On the minimum of independent geometrically distributed random variables

Author

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  • Ciardo, Gianfranco
  • Leemis, Lawrence M.
  • 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.

Suggested Citation

  • Ciardo, Gianfranco & Leemis, Lawrence M. & Nicol, David, 1995. "On the minimum of independent geometrically distributed random variables," Statistics & Probability Letters, Elsevier, vol. 23(4), pages 313-326, June.
    • Handle: RePEc:eee:stapro:v:23:y:1995:i:4:p:313-326
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    Cited by:

    1. Diane L. Evans & Lawrence M. Leemis & John H. Drew, 2006. "The Distribution of Order Statistics for Discrete Random Variables with Applications to Bootstrapping," INFORMS Journal on Computing, INFORMS, vol. 18(1), pages 19-30, February.
    2. Cerchiello, Paola & Giudici, Paolo, 2012. "On the distribution of functionals of discrete ordinal variables," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 2044-2049.

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