Exponentiated $T$-$X$ Family of Distributions with Some Applications

Abstract

In this paper, a new family of distributions called exponentiated T -X distribution is defined. Some of its properties and special cases are discussed. A member of the family, namely, the three-parameter exponentiated Weibullexponential distribution is defined and studied. Some of its properties including distribution shapes, limit behavior, hazard function, Shannon entropy, moments, skewness and kurtosis are discussed. The flexibility of the exponentiated Weibull-exponential distribution is assessed by applying it to three real data sets and comparing it with other distributions. The exponentiated Weibull-exponential distribution is found to adequately fit left-skewed and right-skewed data sets.

A Generalization of the Weibull Distribution with Applications

“…Barreto-Souza et al (2010) applied the beta generalized exponential distribution (BGED) to fit the data and Barreto-Souza, Cordeiro, and Simas (2011) fitted beta Fréchet distribution (BFD) to the data. Recently, Alzaghal, Famoye, and Lee (2013) used the data in an application of the exponentiated Weibull-exponential distribution (EWED). The LWD is fitted to the data and the estimation results and goodness of fit statistics are presented in Table 6.…”

Generalized Transmuted Family of Distributions: Properties and Applications

“…So, several generators based on one or more parameters have been proposed to generate new distributions. Some well-known generators are Marshal-Olkin generated family (MO-G) [33], the beta-G by Eugene et al [20] , Jones [31], Kumaraswamy-G (Kw-G for short) by Cordeiro and de Castro [16], McDonald-G (Mc-G) by Alexander et al [1], gamma-G (type 1) by Zografos and Balakrishanan [57], gamma-G (type 2) by Ristić and Balakrishanan [47] , , gamma-G (type 3) by Torabi and Montazari [55], log-gamma-G by Amini et al [7], logistic-G by Torabi and Montazari [56], exponentiated generalized-G by Cordeiro et al [18], Transformed-Transformer (T-X) by Alzaatreh et al [5], exponentiated (T-X) by Alzaghal et al [6], Weibull-G by Bourguignon et al [12], Exponentiated half logistic generated family by Cordeiro et al [15], Kumaraswamy Odd log-logistic by Alizadeh et al [3], Lomax Generator by Cordeiro et al [19], a new Weibull-G by Tahir et al [51], Logistic-X by Tahir et al [52], Kumaraswamy Marshal-Olkin family by Alizadeh et al [4], Beta Marshal-OLkin family by Alizadeh et al [2], type I half-logistic family by Cordeiro et al [14] and Odd Generalized Exponential family by Tahir et al [53].…”

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.…”