On the Construction of Preliminary Test Estimator Based on Record Values for the Burr XII Model

Abstract

In this paper some different sorts of estimators are proposed based on record breaking observations in the Burr type XII model. We define Bayes as well as empirical Bayes preliminary test estimators in the same fashion as in the ordinary preliminary test estimator using relevant combinations of uniformly minimum variance unbiased (UMVU) and Bayes estimators. Exact and asymptotic bias and mean square error (MSE) expressions for the proposed estimators are derived under two different conditions of knowing the shape parameters. We compare the MSEs and obtain the confidence interval for the parameter of interest in which the preliminary test type estimators outperform the UMVU, Bayes and empirical Bayes estimators.An application of the ordinary preliminary test estimator is also considered. We conclude this approach by a useful discussion for practical purposes and a summary.

Pretest shrinkage estimators for the shape parameter of a Pareto model using prior point knowledge and record observations

“…Prakash and Singh (2007) and Prakash and Singh (2008) dealt with shrinkage pretest estimation under the LINEX loss in Pareto and exponential distribution, respectively. New researches are in works by Belaghi et al(2015), Naghizadeh Qomi and Barmoodeh (2015) and Kiapour and Naghizadeh Qomi (2016).…”

Preliminary test estimators of the reliability characteristics for the three parameters Burr XII distribution based on records

“…Hence it is wise to adopt restricted estimation procedures when we have sufficient confidence in the prior information. Bancroft (1944) introduced the use of PTES and eventually further advancements were proposed by Saleh and Sen (1978), Saleh and Kibria (1993) and Belaghi et al (2014Belaghi et al ( , 2015.…”

“…Chandler (1952) introduced the concept of record values. Based on records, inferential procedures for the parameters of different distributions have been developed by Glick (1978), Nagaraja (1988aNagaraja ( ,1988b), Balakrishan, Ahsanullah and Chan (1995), Arnold, Balakrishan and Nagaraja (1992), Habibi Rad, Arghami and Ahmadi (2006), Arashi and Emadi (2008), Razmkhah and Ahmadi (2011), Belaghi et al (2015) and others.…”

“…( ; , ) = 1 − (1 + ) − ; > 0, , > 0 and ( ; , ) = −1 (1 + ) −( +1) ; > 0, , > 0 Some recent work on Burr XII model can be found in Belaghi and Noori (2016) and Belaghi et al (2017). Belaghi et al (2014Belaghi et al ( , 2015…”

Shrinkage and Bayesian Shrinkage Estimation of the Expected Length of a M/M/1 Queue System

“…wherel is an estimator of l. It is mentioned here that one can consider the pretest estimators which is studied by several authors, see Arabi Belaghi et al (2014Belaghi et al ( , 2015a, Naghizadeh Qomi and Barmoodeh (2015) and Kiapour and Naghizadeh Qomi (2016). But, we focus on Bayesian shrinkage estimation by constructing a class of Bayeasian shrinkage estimators and compare its performance with the MLE.…”