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The Exponentiated Burr XII Power Series Distribution: Properties and Applications

1
Department Statistics, The Islamia University, Bahawalpur 63100, Pakistan
2
Department of Statistics, Mathematics and Insurance, Benha University, Benha 13511, Egypt
3
Department of Measurement and Evaluation, Education Faculty, City Campus, Artvin Çoruh University, 08100 Artvin, Turkey
*
Author to whom correspondence should be addressed.
Stats 2019, 2(1), 15-31; https://doi.org/10.3390/stats2010002
Received: 30 August 2018 / Revised: 17 December 2018 / Accepted: 18 December 2018 / Published: 21 December 2018
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Abstract

In this work, we introduce a new Burr XII power series class of distributions, which is obtained by compounding exponentiated Burr XII and power series distributions and has a strong physical motivation. The new distribution contains several important lifetime models. We derive explicit expressions for the ordinary and incomplete moments and generating functions. We discuss the maximum likelihood estimation of the model parameters. The maximum likelihood estimation procedure is presented. We assess the performance of the maximum likelihood estimators in terms of biases, standard deviations, and mean square of errors by means of two simulation studies. The usefulness of the new model is illustrated by means of three real data sets. The new proposed models provide consistently better fits than other competitive models for these data sets. View Full-Text
Keywords: Burr distribution; compounding; hazard rate; lifetime distribution; maximum likelihood method; power series distribution Burr distribution; compounding; hazard rate; lifetime distribution; maximum likelihood method; power series distribution
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MDPI and ACS Style

Nasir, A.; Yousof, H.M.; Jamal, F.; Korkmaz, M.Ç. The Exponentiated Burr XII Power Series Distribution: Properties and Applications. Stats 2019, 2, 15-31.

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