ON GENERALIZED WEIBULL-RAYLEIGH DISTRIBUTION: ITS PROPERTIES AND APPLICATIONS

Abubakar Yahaya, Alaku Alogala Yohanna

Abstract


Rayleigh distribution as one of the widely used continuous probability distribution was discovered in 1980 by a researcher called Rayleigh. He discovered it from the amplitude of sound resulting from different important sources. The Rayleigh distribution enjoys a wide range of applications comprising life testing experiments, reliability analysis, applied statistics and clinical studies. The distribution is a special case of the two parameter Weibull distribution when the shape parameter
takes on a value 2. In this article, a Generalized Weibull-Rayleigh Distribution
definitions of its probability density function
proposed by earlier research were provided. Some properties of the new distribution such as moments, moment
generating function, characteristics function, quantile function, survival function, hazard function and order statistics were studied. The estimation of the distribution’s parameters was conducted using the method of maximum likelihood. The performance of the proposed probability distribution distribution using three lifetime datasets. The results obtained indicated that GWRD outperforms other similar distributionscomprising Weibull-Rayleigh, Transmuted Rayleigh and the conventional Rayleigh distributions.


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