A new Weibull-G family of distributions

Yıl 2016, Cilt: 45 Sayı: 2, 629 - 647, 01.04.2016

M.h. Tahir M. Zubair M. Mansoor Gauss M Cordeiro Morad Alizadehk G. G. Hamedani

Öz

Statistical analysis of lifetime data is an important topic in reliability
engineering, biomedical and social sciences and others. We introduce
a new generator based on the Weibull random variable called the new
Weibull-G family. We study some of its mathematical properties. Its
density function can be symmetrical, left-skewed, right-skewed, bathtub and reversed-J shaped, and has increasing, decreasing, bathtub,
upside-down bathtub, J, reversed-J and S shaped hazard rates. Some
special models are presented. We obtain explicit expressions for the
ordinary and incomplete moments, quantile and generating functions,
Rényi entropy, order statistics and reliability. Three useful characterizations based on truncated moments are also proposed for the new family. The method of maximum likelihood is used to estimate the model
parameters. We illustrate the importance of the family by means of
two applications to real data sets. 

Anahtar Kelimeler

Generating function, hazard function, moment, reliability function, Rényi entropy, Weibull distribution

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