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

Bi and Mukherjea (2011) considered the following problem: If X-1, ..., X-n are indepen- dent Poisson distributed random variables with parameters lambda(1), ..., lambda(n), respectively, then does the distribution of max{X-1, ..., X-n} or of min{X-1 , ..., X-n} uniquely determine the parameters? They proved that the distribution of max{X-1, X-2, X-3} uniquely determines lambda(1), lambda(2) and lambda(3). In this paper, we prove the identifiability problem of parameters from the distribution of max{X-1, ..., X-n} or of min{X-1 , ..., X-n} for any value of n. (C) 2021 Elsevier B.V. All rights reserved.