Improved estimators of the distribution function b

Authors: R Arabi Belaghi M Arashi S M M Tabatabaey

Publish Date: 2014/04/08

Volume: 56, Issue: 2, Pages: 453-477

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Abstract

In this paper we define different types of estimators for the distribution function namely preliminary test PT shrinkage PT SPT Stein type S and Thompson shrinkage TS estimators based on lower record observations and their inter record times Their asymptotic distributional bias and mean square error are explicitly derived The superiority conditions of the new proposed estimators over the existing estimator of distribution function are also obtained It is shown that about the neighborhood of the null hypothesis F 0 the PTE is superior to the SE in the sense of having higher asymptotic relative efficiency Further for the reasonable values of alpha the newly proposed SPT estimator uniformly dominates the nonparametric maximum like likelihood estimators in the literatures A table is also given to be more specifics along the exhibited theoretical results for practical sake Some graphical representations are given as proofs of our assertions A simulation study is also carried out for some life time distribution to examine the accuracy of the proposed estimators with a limited sample size The results show that combination of the parametric and nonparametric estimators will give more efficient estimators This study is finally concluded by applying the theoretic results to a real data setThe authors would like to thank the anonymous referees for constructive and significant comments that have helped in improving the paper we also appreciate Professor N Balakrishnan and S Gulati for their helpful comments and suggestions on an earlier version of this paper

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