Identification of parameters of Poisson distributions by the extreme order statistics
Ping Sun · Communications in Statistics - Simulation and Computation · 2021
Let Poisson variables X1,⋯,Xm be independent and Y1,⋯,Yn be also independent such that each Xi∼P(λi),Yj∼P(μj). We prove that if Xm:m=max{X1,⋯,Xm} and Yn:n=max{Y1,⋯,Yn} have the same distribution, then m = n and {λ1,⋯,λm} = {μ1,⋯,μm}. The weak version in term of minimum statistics is also derived.