Mathematics and Computational Sciences

The complementary geometric Burr X family of distributions with different estimation methods and application

Articles in Press

Document Type : Original Article

Author

Mohammed Elgarhy

Department of Basic Sciences, Higher Institute of Administrative Sciences, Belbeis, AlSharkia, Egypt

https://doi.org/10.30511/mcs.2026.2074211.1494
Abstract
In this article, we thoroughly investigate a family of distributions using the Burr X family and the complementary geometric G family. The new suggested family is called the complementary geometric Burr X family of distributions. Some important functional forms and family features are presented in a generalized form. Three submodels of this family, complementary geometric Burr X exponential, complementary geometric Burr X Rayleigh, and complementary geometric Burr X Lomax distributions are introduced and discussed. The statistical inference of this new family and the complementary geometric Burr X exponential are explored. The desired parameters are estimated using the maximum likelihood, maximum product of spacings, least square, weighted least square, Cram'er-von-Mises, Anderson-Darling, Right-tail Anderson-Darling and Left-tail Anderson-Darling approaches. A simulation experiment is conducted to further validate these estimates. One actual dataset is explored in the field of medical to demonstrate the adaptability and applicability of the proposed new family of distributions. The results show that, compared to other well-known competing distributions, the new suggested distribution can fit the data with greater accuracy.

Keywords

Burr X family
Complementary Geometric-G family
Moments
Simulation
Maximum likelihood estimation
Subjects
Mathematics and Computational Sciences

Articles in Press, Accepted Manuscript
Available Online from 16 October 2026

  • Receive Date 10 October 2025
  • Revise Date 29 September 2026
  • Accept Date 08 October 2026

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