Email this article A Note on Characterizations of the Exponential Distribution*
- Authors: Ushakov N.G.1, Ushakov V.G.2
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Affiliations:
- Norwegian University of Science and Technology, Department of Mathematical Sciences
- Lomonosov Moscow State University, Department of Mathematical Statistics
- Issue: Vol 214, No 1 (2016)
- Pages: 132-138
- Section: Article
- URL: https://ogarev-online.ru/1072-3374/article/view/237340
- DOI: https://doi.org/10.1007/s10958-016-2763-8
- ID: 237340
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Abstract
The following classical characterization of the exponential distribution is well known. Let X1,X2, . . . Xn be independent and identically distributed random variables. Their common distribution is exponential if and only if random variables X1 and n min(X1, . . .,Xn) have the same distribution. In this note we show that the characterization can be substantially simplified if the exponentiality is characterized within a broad family of distributions that includes, in particular, gamma, Weibull and generalized exponential distributions. Then the necessary and sufficient condition is the equality only expectations of these variables. A similar characterization holds for the maximum.
About the authors
N. G. Ushakov
Norwegian University of Science and Technology, Department of Mathematical Sciences
Author for correspondence.
Email: ushakov@math.ntnu.no
Norway, Trondheim
V. G. Ushakov
Lomonosov Moscow State University, Department of Mathematical Statistics
Email: ushakov@math.ntnu.no
Russian Federation, Moscow
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