Transmuted Rayleigh-X Family of Distributions

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Published: 2025-11-24
Keywords:
hazard function, order statistics, entropy, Transform-transformer method

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J. Abdullahi
Department of Statistics, Ahmadu Bello University, Zaria, Nigeria
S. U. Gulumbe
Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Nigeria
U. Usman
Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Nigeria
A. S. Mohammed
Department of Statistics, Ahmadu Bello University, Zaria, Nigeria
A. I. Garba
Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Nigeria

Abstract

Real world phenomena are always described and predicted using distributions, due to these usefulness distributions are developed and studied by different researchers. In this research, we introduced a novel class of Statistical distributions called Transmuted Rayleigh-X (TR-X). The study focused on exploring various statistical properties of the proposed class, including moment, moment generating function, limiting behaviour, quantile function, distribution of order statistics, reliability and order relevant characteristics. For better understanding of the TR-X class of distributions, we generated plots for the cumulative distribution function (CDF), probability density function (PDF), survival and hazard function for a sub-model (Transmuted Rayleigh-Exponential Distribution) within the family. These plots were constructed for different parameters values to visualize how the distribution changes with varying inputs. The sub-model from the family provided valuable insights for potential applications in diverse fields where probability distributions play a crucial role. The performance of the sub-model was tested using two different datasets. The sub model when compared with Exponential and its extensions revealed a better fit for the two datasets. Therefore, this research concludes that the TR-X family of distributions is capable of generating flexible and robust distribution that can be fitted to data of different shapes.

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Vol. 8 No. 1 (2025)

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Articles
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This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

How to Cite

Abdullahi, J., Gulumbe, S., Usman, U., Mohammed, A., & Garba, A. (2025). Transmuted Rayleigh-X Family of Distributions. Benin Journal of Statistics, 8(1), 36-49. https://bjs-uniben.org/index.php/home/article/view/41

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