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The Exponentiated Burr XII Power Series Distribution: Properties and Applications

Author

Listed:
  • Arslan Nasir

    (Department Statistics, The Islamia University, Bahawalpur 63100, Pakistan)

  • Haitham M. Yousof

    (Department of Statistics, Mathematics and Insurance, Benha University, Benha 13511, Egypt)

  • Farrukh Jamal

    (Department Statistics, The Islamia University, Bahawalpur 63100, Pakistan)

  • Mustafa Ç. Korkmaz

    (Department of Measurement and Evaluation, Education Faculty, City Campus, Artvin Çoruh University, 08100 Artvin, Turkey)

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.

Suggested Citation

  • Arslan Nasir & Haitham M. Yousof & Farrukh Jamal & Mustafa Ç. Korkmaz, 2018. "The Exponentiated Burr XII Power Series Distribution: Properties and Applications," Stats, MDPI, vol. 2(1), pages 1-17, December.
    • Handle: RePEc:gam:jstats:v:2:y:2018:i:1:p:2-31:d:192379
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    References listed on IDEAS

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    1. Antonio E. Gomes & Cibele Q. da-Silva & Gauss M. Cordeiro, 2015. "Two Extended Burr Models: Theory and Practice," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(8), pages 1706-1734, April.
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    Cited by:

    1. Gulnaz Raffiq & Iram Sajjad Dar & Muhammad Ahsan Ul Haq & Eduardo Ramos, 2022. "The Marshall–Olkin Inverted Nadarajah–Haghighi Distribution: Estimation and Applications," Annals of Data Science, Springer, vol. 9(6), pages 1323-1338, December.

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