STUDY ON GENERALIZED WEIBULL-RAYLEIGH DISTRIBUTION WITH ITS APPLICATIONS
STUDY ON GENERALIZED WEIBULL-RAYLEIGH DISTRIBUTION WITH ITS APPLICATIONS
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Date
2017-08
Authors
YOHANNA, ALAKU ALOGALA
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Abstract
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 thesis work, a Generalized Weibull-Rayleigh Distribution (GWRD) is presented. The respective definitions of its probability density function (pdf) and cumulative distribution function (cdf) using the generalized family 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 (GWRD) was compared to some other generalizations of Rayleigh distribution using three simulated datasets. The results obtained were compared using the values of the AIC, CAIC, BIC and HQIC of the fitted distributions and it showed that GWRD outperforms other similar distributions comprising Weibull-Rayleigh, Transmuted Rayleigh, Weibull and the conventional Rayleigh distributions.
Description
A DISSERTATION SUBMITTED TO THE SCHOOL OF POSTGRADUATE STUDIES, AHMADU BELLO UNIVERSITY, ZARIA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE AWARD OF MASTER OF SCIENCE DEGREE IN STATISTICS
DEPARTMENT OF STATISTICS, FACULTY OF PHYSICAL SCIENCES, AHMADU BELLO UNIVERSITY, ZARIA, NIGERIA
Keywords
STUDY ON GENERALIZED,, WEIBULL-RAYLEIGH,, DISTRIBUTION,, APPLICATIONS,