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The Burr XII–Gompertz Distribution: A Competing Risks Model With Applications to Lifetime Data

Author

Listed:
  • Bahman Tarvirdizade
  • Salman Babayi

Abstract

In this article, we introduce a novel four‐parameter lifetime distribution that is constructed by compounding the Burr XII and Gompertz models in a sequential system and is known as the Burr XII–Gompertz distribution. The novel model offers a straightforward form of the hazard rate function which is very flexible since it can handle increasing, decreasing, bathtub‐shaped, unimodal, and modified bathtub‐shaped forms for various values of the parameter space. We study several statistical characteristics of the Burr XII–Gompertz distribution containing quantiles, moments, order statistics, mean deviations, and Rényi entropy. Also, we apply the maximum‐likelihood procedure to obtain the point and interval estimation of parameters and evaluate the maximum‐likelihood estimators performances via a Monte Carlo simulation study. Finally, we examine three datasets from medical and reliability studies that exhibit bathtub‐shaped and modified bathtub‐shaped hazard rate functions to demonstrate the superiority of the proposed distribution in comparison with some competitor distributions for both data.

Suggested Citation

  • Bahman Tarvirdizade & Salman Babayi, 2025. "The Burr XII–Gompertz Distribution: A Competing Risks Model With Applications to Lifetime Data," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jjmath:v:2025:y:2025:i:1:n:1313645
    DOI: 10.1155/jom/1313645
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    References listed on IDEAS

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    1. Renata Rojas Guerra & Fernando A. Peña-Ramírez & Gauss M. Cordeiro, 2023. "The Logistic Burr XII Distribution: Properties and Applications to Income Data," Stats, MDPI, vol. 6(4), pages 1-20, November.
    2. Adam Lenart, 2014. "The moments of the Gompertz distribution and maximum likelihood estimation of its parameters," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2014(3), pages 255-277.
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