Estimation of the density and cumulative distribution functions of the exponentiated Burr XII distribution

Amal S. Hassan, Salwa M. Assar, Kareem A. Ali, Heba F. Nagy

The exponentiated Burr Type XII (EBXII) distribution has wide applications in reliability and economic studies. In this article, the estimation of the probability density function and the cumulative distribution function of EBXII distribution is considered. We examine the maximum likelihood estimator, the uniformly minimum variance unbiased estimator, the least squares estimator, the weighted least squares estimator, the maximum product spacing estimator, the Cramér-von-Mises estimator, and the Anderson-Darling estimator. We derive analytical forms for the bias and mean square error. A simulation study is performed to investigate the consistency of the suggested methods of estimation. Data relating to the wind speed and service times of aircraft windshields are used with the studied methods. The simulation studies and real data applications have revealed that the maximum likelihood estimator performs more efficiently than its remaining counterparts.

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Year of publication:	2021
Authors:	Hassan, Amal S. ; Assar, Salwa M. ; Ali, Kareem A. ; Nagy, Heba F.
Published in:	Statistics in transition : an international journal of the Polish Statistical Association and Statistics Poland. - Warszawa : GUS, ISSN 2450-0291, ZDB-ID 2235641-1. - Vol. 22.2021, 4, p. 171-189
Subject:	exponentiated Burr Type XII model \| least squares estimator \| maximum likelihood estimator \| uniform minimum variance unbiased estimator \| weighted least squares estimator \| Schätztheorie \| Estimation theory \| Statistische Verteilung \| Statistical distribution \| Maximum-Likelihood-Schätzung \| Maximum likelihood estimation

Type of publication:	Article
Type of publication (narrower categories):	Aufsatz in Zeitschrift ; Article in journal
Language:	English
Other identifiers:	10.21307/stattrans-2021-044 [DOI] hdl:10419/266288 [Handle]
Source:	ECONIS - Online Catalogue of the ZBW

Persistent link: https://ebvufind01.dmz1.zbw.eu/10012818210