A Mixture of Weibull Distribution and its Inverse: Properties and Estimation

نوع المستند : المقالة الأصلية

المؤلفون

1 . Faculty of Commerce, AL-Azhar University (Tafahna Al-Ashraf Girls’Branch)

2 Faculty of Graduate Studies for statistical research, Cairo University

3 Faculty of Commerce, AL-Azhar University Girls’Branch

المستخلص

 The methods to construct appropriate new models for lifetime data sets are very popular nowadays among the researchers of this area where existed models in the literature are unsuitable for some situations. Among these methods, mixture distributions which are useful in fitting data that is generated by a complex process. Also inverted distributions are useful in modeling data that variable is inherently the reciprocal of a known variable. The Weibull distribution, having the exponential and Rayleigh as special cases, is a very popular distribution for modeling lifetime data and for modeling phenomena with monotone failure rates. It is one of the best known distributions and has wide applications in diverse disciplines. In this paper we propose anew distribution, which is a mixture of weibull and its inverse (MWIW). The main purpose of this paper is to introduce a new mixture of weibull and its inverse distribution as a new model distribution in order to be applied efficiently in lifetime. Two cases are considered when the mixing proporotion is not related to parameter values and when it depends on parameter values. Some properties of the two models with some graphs of density, comulative, hazard and survival functions are discussed.The model parameters are estimated by the method of maximum likelihood estimation. A simulation study is carried out to illustrate the theoretical results of the maximum likelihood estimation. Finally, applications of the two mixtures are illustrated by real data set.
 
 
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