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

Abstract Bi and Mukherjea (2011) considered the following problem: If X 1 , … , X n are independent Poisson distributed random variables with parameters λ 1 , … , λ 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 λ 1 , λ 2 and λ 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 .