The Exponentiated Generalized-G Poisson Family of Distributions

Abstract

Abstract:In this article we propose and study a new family of distributions which is defined by using the genesis of the truncated Poisson distribution and the exponentiated generalized-G distribution. Some mathematical properties of the new family including ordinary and incomplete moments, quantile and generating functions, mean deviations, order statistics and their moments, reliability and Shannon entropy are derived. Estimation of the parameters using the method of maximum likelihood is discussed. Although this generalization technique can be used to generalize many other distributions, in this study we present only two special models. The importance and flexibility of the new family is exemplified using real world data.

A New Flexible Three-Parameter Model: Properties, Clayton Copula, and Modeling Real Data

“…The * and * statistics are given by: * = (1 + 1/2 ) 1/(12 ) + , and: * = ( ) + , We compared the fits of the MOBE-2 distribution with some competitive models, namely: exponential (E (β)), odd Lindley exponential (OLiE), MO exponential (MOE (α, β)), moment exponential (MomE (β)), the logarithmic Burr-Hatke exponential (Log BrHE (β)), generalized MO exponential (GMOE (α, α, β)), beta exponential (BE (a, b, β)), MO-Kumaraswamy exponential (MOKwE (α, a, b, β)), Kumaraswamy exponential (KwE (a, b, β)), and Kumaraswamy MO exponential (KwMOE (α, a, b, β)). See the PDFs of the competitive moels in [21][22][23][24][25][26][27][28][29][30][31]. We considered the Cramér-Von Mises (W * ), the Anderson-Darling (A * ), and the Kolmogorov-Smirnov (KS) statistics.…”

Type I General Exponential Class of distributions

“…For example, Gupta et al (1998) proposed the exponentiated-G class, which consists of raising the cumulative distribution function (cdf) to a positive power parameter. Many other classes can be cited such as the Marshall-Olkin-G family by Marshall and Olkin (1997), beta generalized-G family by Eugene et al (2002), a new method for generating families of continuous distributions by Alzaatreh et al (2013), exponentiated T-X family of distributions by Alzaghal et al (2013), transmuted exponentiated generalized-G family by Yousof et al (2015), Kumaraswamy transmuted-G by Afify et al (2016b), transmuted geometric-G by Afify et al (2016a), Burr X-G by Yousof et al (2016), exponentiated transmuted-G family by Merovci et al (2016), oddBurr generalized family by Alizadeh et al (2016a) the complementary generalized transmuted poisson family by Alizadeh et al (2016b), transmuted Weibull G family by Alizadeh et al (2016c), the Type I half-logistic family by Cordeiro et al (2016a), the Zografos-Balakrishnan odd log-logistic family of distributions by Cordeiro et al (2016b), generalized transmuted-G by Nofal et al (2017), the exponentiated generalized-G Poisson family by Aryal and Yousof (2017) and beta transmuted-H by Afify et al (2017), the beta Weibull-G family by Yousof et al (2017), among others. This paper is organized as follows.…”

The Exponential Lindley Odd Log-Logistic-G Family: Properties, Characterizations and Applications

“…These generalized distributions give more flexibility by adding one or more parameters to the baseline model. Many classes can be cited such as the Marshall-Olkin-G family by Marshall and Olkin [25], transmuted exponentiated generalized-G family by Yousof et al [34], Burr X-G by Yousof et al [35], type I half-logistic family by Cordeiro et al [12], Zografos-Balakrishnan odd log-logistic family of distributions by Cordeiro et al [13], a new generalized two-sided family of distributions by Korkmaz and Genç [22], generalized odd log-logistic family by Cordeiro et al [10], odd-Burr generalized family by Alizadeh et al [4], beta Weibull G by Yousof et al [36], exponentiated generalized-G Poisson family by Aryal and Yousof [8], type I general exponential class by Hamedani et al [20] and beta transmuted-H by Afify et al [2] among others.…”