Comparison of Lower Bounds for the Variance of Unbiased Estimators for some Well-known Families of Distributions

Nayeban S., Rezaei Roknabadi A. H. and Mohtashami Borzadaran G. R. ()
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Nayeban S.: Department of Statistics, School of Mathematical Sciences, Ferdowsi University of Mashhad, P.O. Box 91775-1159, Mashhad, Iran
Rezaei Roknabadi A. H.: Department of Statistics, School of Mathematical Sciences, Ferdowsi University of Mashhad, P.O. Box 91775-1159, Mashhad, Iran
Mohtashami Borzadaran G. R.: Department of Statistics, School of Mathematical Sciences, Ferdowsi University of Mashhad, P.O. Box 91775-1159, Mashhad, Iran

Stochastics and Quality Control, 2013, vol. 28, issue 2, 89-95

Abstract: One of the most fundamental issues in estimation theory about accuracy of an unbiased estimator is computing or approximating its variance. Very often, the variance has a complicated form or cannot be computed explicitly. In this paper, we consider two well-known lower bounds for the variance of unbiased estimator, namely the Bhattacharyya (1946, 1947) and the Kshirsagar (2000) bounds for some versatile families of distributions in statistics and especially in reliability analysis. We consider the generalized gamma (GG), inverse Gaussian, Burr type XII and Burr type III distributions, and derive for these distributions, general forms of Bhattacharyya and Kshirsagar matrices. Additionally, we evaluate different Bhattacharyya and Kshirsagar bounds for the variance of estimators of some functions of relevant parameters and arrive at proposal which of the bounds should be used in given situations.

Keywords: Bhattacharyya Bound; Cramèr-Rao Bound; Generalized Gamma Distribution; Hammersley-Chapman-Robins Bound; Inverse Gaussian Distribution; Burr Type III Distribution; Burr Type XII Distribution; Kshirsagar Bound; Bhattacharyya Bound; Cramèr-Rao Bound; Generalized Gamma Distribution; Hammersley-Chapman-Robins Bound; Inverse Gaussian Distribution; Burr Type III Distribution; Burr Type XII Distribution; Kshirsagar Bound (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1515/eqc-2013-0016

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