A New Compound Family of Weibull Order Statistics and Left k-Truncated Power Series Distributions

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-23-2025-106
Published: May 8, 2025
Cite as:
Mohieddine Rahmouni, A New Compound Family of Weibull Order Statistics and Left k-Truncated Power Series Distributions, Int. J. Anal. Appl., 23 (2025), 106.

Main Article Content

Mohieddine Rahmouni

Abstract

This paper introduces a new family of distributions by compounding the left k-truncated power series distribution with the k-th order statistic of the Weibull distribution. The new family provides a flexible framework for modeling complex data, particularly in reliability engineering and survival analysis. We derive key functions, including the probability density function (PDF), cumulative distribution function (CDF), and hazard rate function (HRF). Several important special cases—such as the geometric, Poisson, binomial, and logarithmic power series distributions—are discussed. Fundamental properties of the family, including moments and quantiles, are explored. Parameter estimation is addressed using the maximum likelihood and the expectation-maximization methods. The paper concludes with potential applications and future research directions.

Article Details

References

  1. M. Goldoust, S. Rezaei, Y. Si, S. Nadarajah, Lifetime Distributions Motivated by Series and Parallel Structures, Commun. Stat. - Simul. Comput. 48 (2019), 556–579. https://doi.org/10.1080/03610918.2017.1390122.
  2. 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.
  3. M. Imran, N. Alsadat, M.H. Tahir, et al. The Development of an Extended Weibull Model with Applications to Medicine, Industry and Actuarial Sciences, Sci. Rep. 14 (2024), 12338. https://doi.org/10.1038/s41598-024-61308-8.
  4. 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.
  5. G.S. Mudholkar, D.K. Srivastava, Exponentiated Weibull Family for Analyzing Bathtub Failure-Rate Data, IEEE Trans. Reliab. 42 (1993), 299–302. https://doi.org/10.1109/24.229504.
  6. 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 92 (2005), 505–505. https://doi.org/10.1093/biomet/92.2.505.
  7. W. Lu, D. Shi, A New Compounding Life Distribution: The Weibull–Poisson Distribution, J. Appl. Stat. 39 (2012), 21–38. https://doi.org/10.1080/02664763.2011.575126.
  8. W. Barreto-Souza, A.L. De Morais, G.M. Cordeiro, The Weibull-Geometric Distribution, J. Stat. Comput. Simul. 81 (2011), 645–657. https://doi.org/10.1080/00949650903436554.
  9. 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.
  10. M. Rahmouni, A. Orabi, A Generalization of the Exponential-Logarithmic Distribution for Reliability and Life Data Analysis, Life Cycle Reliab. Saf. Eng. 7 (2018), 159–171. https://doi.org/10.1007/s41872-018-0049-5.
  11. M. Rahmouni, A. Orabi, The Exponential-Generalized Truncated Geometric (EGTG) Distribution: A New Lifetime Distribution, Int. J. Stat. Probab. 7 (2017), 1. https://doi.org/10.5539/ijsp.v7n1p1.
  12. M. Rahmouni, A. Orabi, A Reverse Exponential-Generalized Truncated Logarithmic (Rev-EGTL) Distribution For Ordered Spacing Statistics, J. Stat. Appl. Probab. 12 (2023), 39–48. https://doi.org/10.18576/jsap/120104.