Abstract: Consider independent
left-truncated modified power series populations with functions of parameter From each population we
have nindependent observations and let denote the sum of these
observations. For selecting the best population, the one associated with the
smallest parameter (largest parameter we
consider the natural selection rule which selects the population if and only if Since our problem is in the discrete case, there is a high probability of
existing ties in the values of so, we break these ties by
selecting the population with the smallest index among the tied populations. In
this paper, we consider the problem of estimating the function of parameter of
the selected population under the entropy loss function and prove
inadmissibility of the natural estimator by constructing two different classes
of improved estimators. In particular, improved estimators of for the selected left-truncated generalized Poisson distribution are also
presented.
Keywords and phrases: estimation after selection, entropy loss function, difference inequalities, truncated modified power series distributions.
