The Burr X Generator of Distributions for Lifetime Data

Abstract

In this paper, we introduce a new class of distributions called the Burr X family. Some of its mathematical and structural properties are derived. The maximum likelihood is used for estimating the model parameters. The importance and flexibility of the new family are illustrated by means of an application to real data set.

The Complementary Generalized Transmuted Poisson-G Family of Distributions

“…The extra parameters of a good generator can usually give lighter tails and heavier tails, accommodate unimodal, bimodal, symmetric, bimodal and right-skewed and bimodal and left-skewed density function, increase and decrease skewness and kurtosis and, more important, yield the four types of the hazard function (increasing, decreasing, bathtub and unimodal). There are several well-known generators such as the following ones: the Marshall-Olkin-G by Marshall and Olkin (1997), beta-G by Eugene, Lee, and Famoye (2002), Kumaraswamy-G by Cordeiro and de Castro (2011), McDonald-G by Alexander, Cordeiro, Ortega, and Sarabia (2012), gamma-G by Zografos and Balakrishnan (2009), Kumaraswamy odd log-logistic-G by Alizadeh, Emadi, Doostparast, Cordeiro, Ortega, and Pescim (2015), beta odd log-logistic generalized by Cordeiro et al (2015), transmuted exponentiated generalized-G by Yousof, Afify, Alizadeh, Butt, Hamedani, and Ali (2015), generalized transmuted-G Nofal, Afify, Yousof, and , transmuted geometric-G by Afify, Alizadeh, Yousof, Aryal, and Ahmad (2016a), Kumaraswamy transmuted-G by Afify, Cordeiro, Yousof, Alzaatreh, and Nofal (2016b), beta transmuted-H by Afify, Yousof, and Nadarajah (2017), Burr X-G by Yousof, Afify, Hamedani, and Aryal (2016) and odd-Burr generalized-G by Alizadeh, Cordeiro, Nascimento, Lima, and Ortega (2017) families, among others.…”

Characterizations and Infinite Divisibility of Certain Recently Introduced Distributions IV

“…The BXEF distribution of Zayed and Butt (2017) is a submodel of BX-G distribution introduced by Yousof et al (2016), which has been characterized in Hamedani (2017a).…”

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.…”