Simultaneous estimation of Poisson means of the selected subset

Let π1,π2,…,πp be p independent Poisson populations with means λ1,…,λp, respectively. Let {X1,…,Xp} denote the set of observations, where Xi is from πi. Suppose a subset of populations is selected using Gupta and Huang's (1975) selection rule which selects πi if and only if Xi+1⩾cX(1), where X(1)=max{X1,…,Xp}, and 0