Marshall-Olkin Power Rayleigh Distribution with Properties and Engineering Applications | ||||
| The Egyptian Statistical Journal | ||||
| Article 3, Volume 68, Issue 1, June 2024, Page 26-44 PDF (652.06 K) | ||||
| Document Type: Original Article | ||||
| DOI: 10.21608/esju.2024.249959.1022 | ||||
 View on SCiNiTO | ||||
| Author | ||||
Yassmen Y. Abdelall 
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| Mathematical statistics department, faculty of graduate studies and statistical research, Cairo university, Egypt | ||||
| Abstract | ||||
| This study presents the proposal of a novel three-parameter Rayleigh distribution, namely Marshall-Olkin Power Rayleigh (MOPR) distribution. Marshall-Olkin Rayleigh (MOR), Marshall-Olkin Chi-Square, and Power Rayleigh (PR) are three particular sub-models of the new distribution. Several of its statistical and mathematical characteristics are derived such as explicit moments, mean deviation, quantile function, Rényi entropy measure, order statistics densities and maximum likelihood estimators. The new distribution may be more flexible since the density shapes are symmetrical and left skewed. The reverse hazard function and truncated moments have been used to obtain the characterizations of the suggested distribution. A Monte Carlo simulation has been conducted to assess maximum likelihood estimators' consistency with respect to bias, variance, and mean square error (MSE) measures. In the end, the proposed distribution is applied to an engineering science-related real data sets and it is seen that this distribution is a flexible model that may be a useful alternative to known distributions like Rayleigh, and Power Rayleigh distributions. | ||||
| Keywords | ||||
| Marshall-Olkin; Power Rayleigh distribution; moments; order statistic; maximum likelihood method | ||||
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