Title: A class of always pooling shrinkage testimators for the Weibull model

Authors: Zuhair A. Al-Hemyari; H.A. Al-Dabag; Ali Al-Humairi

Addresses: Ministry of Higher Education, P.O. Box 82, P.C. 112, Ruwi, Sultanate of Oman ' College of Education, Babil University, Babil, Iraq ' Department of Computer Science, German University of Technology, Oman; Department of Communication Technologies, University of Duisburg-Essen, Duisburg, Germany

Abstract: Utilising the prior information or additional information from the past in new estimation processes has been receiving considerable attention in the last few decades - as such appears from the list of the references of this paper. In fact, the shrinkage testimators were developed originally for the purpose of utilising the prior information in new estimation problems. In this paper, we have developed a general class of shrinkage testimator, and because it always uses the prior value, are called the always pooling shrinkage testimator for any parameter or distribution. The expressions of bias, risk, risk ratio, relative efficiency, region and shrinkage weight function are derived. The dual importance of the proposed class of testimators are in using the prior information in both stages, something which has significant influence in increasing the relative efficiency and reduction of the sample size required. The comparisons, recommendations, discussions and limitations are provided in this paper.

Keywords: always pooling; shrinkage; Weibull failure model; shape parameter; censored data; bias ratio; relative risk.

DOI: 10.1504/IJMOR.2019.099387

International Journal of Mathematics in Operational Research, 2019 Vol.14 No.3, pp.407 - 432

Received: 27 Apr 2017
Accepted: 29 Oct 2017
Published online: 01 May 2019 *

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