Abstract
In this study, we introduce a new family of models for lifetime data called generalized extended Weibull power series family of distributions by compounding generalized extended Weibull distributions and power series distributions. The compounding procedure follows the same setup carried out by Adamidis (1998). The proposed family contains all types of combinations between truncated discrete with generalized and non-generalized Weibull distributions. Some existing power series and subclasses of mixed lifetime distributions become special cases of the proposed family, such as the compound class of extended Weibull power series distributions proposed by Silva et al. (2013) and the generalized exponential power series distributions introduced by Mahmoudi and Jafari (2012). Some mathematical properties of the new class are studied, including the cumulative distribution function, density function, survival function, and hazard rate function. The method of maximum likelihood is used for obtaining a general setup for estimating the parameters of any distribution in this class. An expectation-maximization algorithm is introduced for estimating maximum likelihood estimates. Special subclasses and applications for some models in a real dataset are introduced to demonstrate the flexibility and the benefit of this new family.
Highlights
The modeling and analysis of lifetimes is an important aspect of statistical work in a wide variety of scientific and technological fields, such as public health, actuarial science, biomedical studies, demography, and industrial reliability
We combine the generalized exponential power series (GEPS) distributions introduced by Mahmoudi and Jafari (2012) and the compound class of the extended Weibull power series distributions (EWPS) proposed by Silva et al (2013) into a more general family called the generalized extended Weibull power series (GEWPS)
By taking a system with parallel components in which the random variable N has the power series distributions and the random variable X i follows the generalized Weibull distribution, we introduce the GEWPS class of distributions that contain the GEPS and the EWPS distributions as special cases
Summary
The modeling and analysis of lifetimes is an important aspect of statistical work in a wide variety of scientific and technological fields, such as public health, actuarial science, biomedical studies, demography, and industrial reliability. We combine the GEPS distributions introduced by Mahmoudi and Jafari (2012) and the compound class of the extended Weibull power series distributions (EWPS) proposed by Silva et al (2013) into a more general family called the generalized extended Weibull power series (GEWPS). The proposed family can be applied to other fields, including business, environment, actuarial science, biomedical studies, demography and industrial reliability, and many other fields This family contains several subclasses and lifetime models as special cases. By taking a system with parallel components in which the random variable N has the power series distributions and the random variable X i follows the generalized Weibull distribution, we introduce the GEWPS class of distributions that contain the GEPS and the EWPS distributions as special cases. By using the idea of Gupta and Cundu (1999), the generalized exponential of this class can be modified as follows: Definition 2: A random variable X i belongs to the generalized extended Weibull distribution class if its cdf is given by
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