Identification of parameters from the distribution of the maximum or minimum of Poisson random variables

Bara Kim and Jeongsim Kim

Statistics & Probability Letters, 2022, vol. 180, issue C

Abstract: Bi and Mukherjea (2011) considered the following problem: If X1,…,Xn are independent Poisson distributed random variables with parameters λ1,…,λn, respectively, then does the distribution of max{X1,…,Xn} or of min{X1,…,Xn} uniquely determine the parameters? They proved that the distribution of max{X1,X2,X3} uniquely determines λ1,λ2 and λ3. In this paper, we prove the identifiability problem of parameters from the distribution of max{X1,…,Xn} or of min{X1,…,Xn} for any value of n.

Keywords: Poisson distributions; Identification of parameters; Distribution of maximum; Distribution of minimum (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spl.2021.109243

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