Generalized extended Weibull power series family of distributions

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.

Harmonic Mixture Weibull-G Family of Distributions: Properties, Regression and Applications to Medical Data

“…Consequently, new families of distributions in the form of extended or modified versions of the Weibull distribution have been introduced in literature with the attempt of increasing its flexibility. Some examples include the following: Marshall-Olkin Weibull generated family [2], exponentiated power generalized Weibull power series family of distributions [3], complementary generalized power Weibull power series family of distributions [4], the Burr-Weibull power series family [5], extended Weibull-G family [6], Weibull Burr X-G family of distributions [7], the Weibull Marshall-Olkin family [8], the gamma-Weibull-G family [9], generalized odd Weibull generated family [10], the beta Weibull-G family [11], Kumaraswamy Weibullgenerated family [12], generalized extended Weibull power series family of distributions [13], the inverse Weibull power series family [14], the Marshall-Olkin extended Weibull family of distributions, [15] and the extended Weibull power series family [16].…”

Generalized inverse Lindley power series distributions: modeling and simulation

“…These distributions were obtained by compounding some useful lifetime distributions with power series distributions. Lindley power series (LPS) class of distributions (Liyanage and Pararai [22]), Weibull power series class of distributions (Morais and Barreto-Souza [25]), compound class of extended Weibull power series of distributions (Silva et al [31]), a generalization of the extended Weibull power series family of distributions (Alkarni [2]), exponentiated extended Weibull power series class of distributions (Tahmasebi and Jafari [33]), inverse Weibull power series distributions (Shafie et al [27]), generalized exponential power series of distributions (Mahmoudi and Jafari [23]), complementary exponential power series (Flores et al [14]), double-bounded Kumaraswamy power series (Bidram and Nekoukhou [6]), Burr XII power series (Silva and Cordeiro [32]), generalized linear failure rate power series of distributions (Alamatsaz and Shams [16]), Birnbaum Saunders power series of distribution (Bourguignon et al [7]), linear failure rate-power series of distributions (Mahmoudi and Jafari [24]), complementary extended Weibull-power series of distributions (Cordeiro and Silva [8]), Gompertz-power series distributions (Tahmasebi and Jafari [19]), the Exponential Pareto power series distribution (Elbatal et al [13]), generalized modified Weibull power series distribution (Bagheri et al [4]), Compound family of generalized inverse Weibull power series distributions (Hassan et al [18]), and complementary exponentiated inverted Weibull power series family of distributions (Hassan et al [17]) are some examples of such distributions. To compound a continuous distribution with a discrete one, Nadarajah et al [26] introduced the package: Compounding in R software (R Development Core Team [34]).…”