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A New Rayleigh Distribution: Properties and Estimation Based on Progressive Type-II Censored Data with an Application

Ali Algarni, Abdullah M. Almarashi*
Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia
* Corresponding Authors: Abdullah M. Almarashi. Email: ,
(This article belongs to this Special Issue: New Trends in Statistical Computing and Data Science)

Computer Modeling in Engineering & Sciences 2022, 130(1), 379-396.

Received 31 May 2021; Accepted 04 August 2021; Issue published 29 November 2021


In this paper, we propose a new extension of the traditional Rayleigh distribution called the modified Kies Rayleigh distribution. The new distribution contains one scale and one shape parameter and its hazard rate function can be increasing and bathtub-shaped. Some mathematical properties of the new distribution are derived including quantiles and moments. The parameters of modified Kies Rayleigh distribution are estimated based on progressively Type-II censored data. For this purpose, we consider two estimation methods, namely maximum likelihood and maximum product of spacing estimation methods. To compare the efficiency of the proposed estimators, a simulation study is carried out. To show the applicability of the new model as well as the estimation methods, one real data for failure times of software is analyzed. Based on the empirical parts, we can conclude that the proposed model can be considered as a good model in the field of life testing and reliability analysis compared with other competing models.


Rayleigh distribution; modified kies family; progressive Type-II censored; maximum likelihood estimation; maximum product of spacing

Cite This Article

Algarni, A., Almarashi, A. M. (2022). A New Rayleigh Distribution: Properties and Estimation Based on Progressive Type-II Censored Data with an Application. CMES-Computer Modeling in Engineering & Sciences, 130(1), 379–396.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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