Generalized Weibull Distribution Revisited - Sewilam, Eman M. (جامعة المنوفية - كلية التجارة, 2008)
In an earlier work by Soleha and Sewilam (2007), an entropy transformation, g(x), using the reliability function and the cumulative distribution function of a continuous random variable is suggested. It is implemented considering the Rayleigh distribution. The derivative, g;(x), gives a peculiar form which is found to be a density function. The present study is a trial to generalize the idea by studying the Weibull distribution. The resulting form is found to be a density function. A statistical inference about the behavior of the derived density function is presented. The main properties of this density function are provided. The behavior of its hazard (failure) rate is investigated. The rth moment of a continuous random variable of the derived density function is obtained. The results are verified with the results of the Rayleigh distribution presented by Soleha and Sewilam (2007), considering the Rayleigh distribution as a special case of the Weibull distribution. A peculiar form of the exponential distribution is derived as another special case of the Weibull distribution. The behavior of the derived density function, the reliability function and the hazard (failure) rate has been compared with the behavior of the corresponding well known Weibull distribution.
Keywords: النشاط التجاري -- معمم يبل -- الإحصاء