Mathematics and Statistics Vol. 12(2), pp. 184 - 198
DOI: 10.13189/ms.2024.120208
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A Class of Efficient Shrinkage Estimators for Modelling the Reliability of Burr XII Distribution

Zuhair A. Al-Hemyari ^1,*, Alaa Khlaif Jiheel ², Iman Jalil Atewi ^2
1 Department of Mathematical and Physical Sciences, CAS, University of Nizwa, Oman
² Department of Mathematics, College of Education for Pure Sciences, University of Thi-Qar, Iraq

ABSTRACT

For the purpose of modelling the Reliability of Burr XII Distribution, a family of shrinkage estimators is proposed for any parameter of any distribution when a prior guess value of is available from the past. In addition, two sub-models of the shrinkage type estimators for estimating the reliability and parameters of the Burr XII Distribution using two types of shrinkage weight functions with the preliminary test of the hypothesis against the alternative have been proposed and studied. The criteria for studying the properties of two sub-models of the reliability estimators which are the Bias, Bias ratio, Mean Squared Error and Relative Efficiency were derived and computed numerically for each sub-model for the purpose of studying the behavior of the estimators for the Burr XII Distribution because they are complicated and contain many complex functions. The numerical results showed the usefulness of the proposed two sub-models of the reliability estimators of Burr XII Distribution relative to the classical estimators for both of the shrinkage functions when the value of the a priori guess value is close to the true value of . In addition, the comparison between the proposed two sub-models of the shrinkag

KEYWORDS
Modelling, Shrinkage, Reliability, Burr XII Distribution, Relative Efficiency

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Zuhair A. Al-Hemyari , Alaa Khlaif Jiheel , Iman Jalil Atewi , "A Class of Efficient Shrinkage Estimators for Modelling the Reliability of Burr XII Distribution," Mathematics and Statistics, Vol. 12, No. 2, pp. 184 - 198, 2024. DOI: 10.13189/ms.2024.120208.

(b). APA Format:
Zuhair A. Al-Hemyari , Alaa Khlaif Jiheel , Iman Jalil Atewi (2024). A Class of Efficient Shrinkage Estimators for Modelling the Reliability of Burr XII Distribution. Mathematics and Statistics, 12(2), 184 - 198. DOI: 10.13189/ms.2024.120208.