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The Opone family of distributions. Beyond the power continuous Bernoulli distribution

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  • Festus C. Opone
  • Christophe Chesneau

Abstract

Recent developments in applied statistics have given rise to the continuous Bernoulli distribution, a one-parameter distribution with support of [0, 1]. In this paper, we use it for a more general purpose: the creation of a family of distributions. We thus exploit the flexible functionalities of the continuous Bernoulli distribution to enhance the modeling properties of well-referenced distributions. We first focus on the theory of this new family, including the quantiles, expansion of important functions, and moments. Then we exemplify it by considering a special baseline: the Topp–Leone distribution. Thanks to the functional structure of the continuous Bernoulli distribution, we create a new two-parameter distribution with support for [0, 1] that possesses versatile shape capacities. In particular, the corresponding probability density function has left-skewed, N-type and decreasing shapes, and the corresponding hazard rate function has increasing and bathtub shapes, beyond the possibilities of the corresponding functions of the Topp– Leone distribution. Its quantile and moment properties are also examined. We then use our modified Topp–Leone distribution from a statistical perspective. The two parameters are supposed to be unknown and then estimated from proportional-type data with the maximum likelihood method. Two different data sets are considered, and reveal that the modified Topp–Leone distribution can fit them better than popular rival distributions, including the unit-Weibull, unit-Gompertz, and log-weighted exponential distributions. It also outperforms the Topp–Leone and continuous Bernoulli distributions.

Suggested Citation

  • Festus C. Opone & Christophe Chesneau, 2024. "The Opone family of distributions. Beyond the power continuous Bernoulli distribution," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 34(4), pages 103-124.
    • Handle: RePEc:wut:journl:v:34:y:2024:i:4:p:103-124:id:7
    DOI: 10.37190/ord240407
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    References listed on IDEAS

    as
    1. M. E. Ghitany & S. Kotz & M. Xie, 2005. "On some reliability measures and their stochastic orderings for the Topp-Leone distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(7), pages 715-722.
    2. Ali Genç, 2012. "Moments of order statistics of Topp–Leone distribution," Statistical Papers, Springer, vol. 53(1), pages 117-131, February.
    3. Emrah Altun, 2021. "The log-weighted exponential regression model: alternative to the beta regression model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(10), pages 2306-2321, May.
    4. J. Mazucheli & A. F. B. Menezes & L. B. Fernandes & R. P. de Oliveira & M. E. Ghitany, 2020. "The unit-Weibull distribution as an alternative to the Kumaraswamy distribution for the modeling of quantiles conditional on covariates," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(6), pages 954-974, April.
    5. Festus C. Opone & Nosakhare Ekhosuehi & Sunday E. Omosigho, 2022. "Topp-Leone Power Lindley Distribution(Tlpld): its Properties and Application," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 597-608, August.
    6. Rashad A. R. Bantan & Farrukh Jamal & Christophe Chesneau & Mohammed Elgarhy, 2021. "Theory and Applications of the Unit Gamma/Gompertz Distribution," Mathematics, MDPI, vol. 9(16), pages 1-22, August.
    7. Saralees Nadarajah & Samuel Kotz, 2003. "Moments of some J-shaped distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(3), pages 311-317.
    8. Josmar Mazucheli & André Felipe Menezes & Sanku Dey, 2019. "Unit-Gompertz Distribution with Applications," Statistica, Department of Statistics, University of Bologna, vol. 79(1), pages 25-43.
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