On Bayesian optimum allocation in some two phase sampling problems

Summary For estimating certain parametric functions, we consider the problem of allocatingN_i, the size of the sample from theith population,i=1,2,...,k, at the second phase of sampling of a two phase sampling procedure, given that we taken_i observations from the population at the first phase. We consider that the observations from theith population follow the exponential distribution with mean _i,i=1,2,...,k, and the functions to be estimated are (i) (d_i/_i) and (ii) (d_ii). When the total cost of sampling at the second phase is c_iN_i and is fixed, allocations using the Bayes approach are obtained so that the estimation is as precise as is possible.