On the identity of the smallest random variable

Yigal Gerchak; Qi Ming He

doi:10.1023/A:1013974510215

On the identity of the smallest random variable

Yigal Gerchak, Qi Ming He

Department of Industrial Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

We compute and analyze the probability that a particular random variable will assume the smallest value among a set of random variables. This work was motivated by wanting to predict the "winner" in R&D and patent "races". Some general results and comparative statistics are provided. For symmetric distributions we derive bounds on the probabilities of interest. We compute the probabilities of who will be the smallest (fastest) for normal, lognormal, Weibull, Pareto, binomial and PH-distributions. We also analyze several models of multivariate exponential distributions.

Original language	English
Pages (from-to)	559-564
Number of pages	6
Journal	IIE Transactions (Institute of Industrial Engineers)
Volume	34
Issue number	6
DOIs	https://doi.org/10.1023/A:1013974510215
State	Published - Jun 2002

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On the identity of the smallest random variable

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