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The four-parameter Burr XII distribution: Properties, regression model, and applications

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  • Ahmed Z. Afify
  • Gauss M. Cordeiro
  • Edwin M. M. Ortega
  • Haitham M. Yousof
  • Nadeem Shafique Butt

Abstract

This paper introduces a new four-parameter lifetime model called the Weibull Burr XII distribution. The new model has the advantage of being capable of modeling various shapes of aging and failure criteria. We derive some of its structural properties including ordinary and incomplete moments, quantile and generating functions, probability weighted moments, and order statistics. The new density function can be expressed as a linear mixture of Burr XII densities. We propose a log-linear regression model using a new distribution so-called the log-Weibull Burr XII distribution. The maximum likelihood method is used to estimate the model parameters. Simulation results to assess the performance of the maximum likelihood estimation are discussed. We prove empirically the importance and flexibility of the new model in modeling various types of data.

Suggested Citation

  • Ahmed Z. Afify & Gauss M. Cordeiro & Edwin M. M. Ortega & Haitham M. Yousof & Nadeem Shafique Butt, 2018. "The four-parameter Burr XII distribution: Properties, regression model, and applications," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(11), pages 2605-2624, June.
    • Handle: RePEc:taf:lstaxx:v:47:y:2018:i:11:p:2605-2624
    DOI: 10.1080/03610926.2016.1231821
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    Cited by:

    1. Broderick Oluyede & Thatayaone Moakofi, 2023. "The Gamma-Topp-Leone-Type II-Exponentiated Half Logistic-G Family of Distributions with Applications," Stats, MDPI, vol. 6(2), pages 1-28, June.
    2. Lucas D. Ribeiro Reis & Gauss M. Cordeiro & Maria do Carmo S. Lima, 2022. "The Stacy-G Class: A New Family of Distributions with Regression Modeling and Applications to Survival Real Data," Stats, MDPI, vol. 5(1), pages 1-43, March.
    3. 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.
    4. Ibrahim Elbatal & Emrah Altun & Ahmed Z. Afify & Gamze Ozel, 2019. "The Generalized Burr XII Power Series Distributions with Properties and Applications," Annals of Data Science, Springer, vol. 6(3), pages 571-597, September.
    5. Abdul Ghaniyyu Abubakari & Claudio Chadli Kandza-Tadi & Edwin Moyo, 2023. "Modified Beta Inverse Flexible Weibull Extension Distribution," Annals of Data Science, Springer, vol. 10(3), pages 589-617, June.

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