The Doubly Generalized Weibull Power Series Frailty Distribution

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-23-2025-255
Published: Oct 16, 2025
Cite as:
Mohieddine Rahmouni, The Doubly Generalized Weibull Power Series Frailty Distribution, Int. J. Anal. Appl., 23 (2025), 255.

Main Article Content

Mohieddine Rahmouni

Abstract

This paper introduces the doubly generalized Weibull power series frailty (DGWPSF) model, an extension of the Weibull–k-truncated power series family incorporating a gamma-frailty term. The model enhances flexibility for lifetime data by accommodating unobserved heterogeneity and latent risk factors in survival and reliability studies. We derive its fundamental properties, including the probability density, distribution, survival, and hazard functions, and highlight notable special cases, including the binomial, Poisson, geometric, and logarithmic models. To address the challenges of parameter estimation, we develop the expectation-maximization algorithm and the Bayesian inference procedures. The DGWPSF framework offers a flexible structure for lifetime data analysis, capturing diverse frailty patterns while improving model interpretability and robustness.

Article Details

References

  1. G. Mudholkar, D. Srivastava, Exponentiated Weibull Family for Analyzing Bathtub Failure-Rate Data, IEEE Trans. Reliab. 42 (1993), 299–302. https://doi.org/10.1109/24.229504.
  2. A.W. Marshall, I. Olkin, A New Method for Adding a Parameter to a Family of Distributions with Application to the Exponential and Weibull Families, Biometrika 84 (1997), 641–652. https://www.jstor.org/stable/2337585.newpage.
  3. M.H. Tahir, G.M. Cordeiro, Compounding of Distributions: A Survey and New Generalized Classes, J. Stat. Distrib. Appl. 3 (2016), 13. https://doi.org/10.1186/s40488-016-0052-1.
  4. M. Rahmouni, A New Compound Family of Weibull Order Statistics and Left K-Truncated Power Series Distributions, Int. J. Anal. Appl. 23 (2025), 106. https://doi.org/10.28924/2291-8639-23-2025-106.
  5. P. Hougaard, Analysis of Multivariate Survival Data, Springer New York, 2000. https://doi.org/10.1007/978-1-4612-1304-8.
  6. L. Duchateau, P. Janssen, The Frailty Model, Springer, (2008).
  7. A.L. Morais, W. Barreto-Souza, A Compound Class of Weibull and Power Series Distributions, Comput. Stat. Data Anal. 55 (2011), 1410–1425. https://doi.org/10.1016/j.csda.2010.09.030.
  8. M. Rahmouni, D. Ziedan, The Weibull-Generalized Shifted Geometric Distribution: Properties, Estimation, and Applications, AIMS Math. 10 (2025), 9773–9804. https://doi.org/10.3934/math.2025448.
  9. H.A. David, H.N. Nagaraja, Order Statistics, Wiley, 2003.
  10. A. Rényi, On the Theory of Order Statistics, Acta Math. Acad. Sci. Hung. 4 (1953), 191–231. https://doi.org/10.1007/bf02127580.