A modified T-X family of distributions: classical and Bayesian analysis

Abstract

In this article, we propose a new family of distributions, namely, a modified T-X family of distributions. The case of the newly proposed family is advocated with respect to three most attractive features: flexibility, efficiency and parsimony. The statistical features are established through simulation studies. The applicability of the scheme is further assessed by using two diverse data sets. The performance evaluation study is conducted with respect to five existing distributions while considering various goodness-of-fit criteria. Moreover, the estimation of the parameters is delineated under the classic approach and Bayesian framework. Based on the findings of this research, we see our proposition as a more efficient and parsimonious alternative to the existing well-known cubic transmutation family of distributions. Finally, the flexible nature of the devised family of distributions may project as a useful candidate in survival analysis and reliability theory. ARTICLE HISTORY

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“…A new family which is named as modified {T-X} family is proposed by Aslam et al [32]. The estimation studies are conducted and for the goodness of fit criteria compare the distribution with five existing distributions.…”

“…The beta-G is studied by Eugene et al [6], betanormal by Eugene et al [7], normal and student´s t distribution studied by Ahsanullah et al [8], a note on a characterization of Gompertz-Verhulst Distribution by Ahsanullah et al [9], Kumaraswamy-G studied by Cordeiro et al [10], the Weibull-G studied by Bourguignon et al [11], the exponentiated half-logistic family studied by Cordeiro et al [12], log-gamma-G by Amini et al [13], Gamma-Pareto distribution considered by Alzaatreh et al [14], Gamma half-Cauchy Alzaatreh et al [15], Gamma Normal by Alzaatreh et al [16], Weibull-X family of distributions studied by Alzaatreh et al [17], Exponentiated generalized class by Cordeiro et al [18], exponentiated {T-X}by Alzaghal et al [19], family of gamma-X by Alzaatreh et al [20], gamma logistic by Alzaatreh et al [21], logistic-G by Torabi et al [22], type-I half-logistic family by Cordeiro et al [23], Kumaraswamy Weibull-generated by Hassan et al [24], generalized Pearson system of distributions by Shakil et al. [25], on a family of product distributions based on the Whittaker functions and generalized Pearson differential equation by Shakil et al [26], generalized transmuted-G by Nofal et al [27], T-transmuted X-family of distribution by Jayakumar and Girish [28], transmuted exponentiated generalized-G by Yousof et al [29], new generalized family of distributions by Ahmad et al [30], some new members of the {T-X} family by Farrukh et al [31], modified {T-X} family by Aslam et al [32], properties and applications of new member of {T-X} family of distributions by Handique et al [33], and exponential {T-X} family of distributions by Zubaira et al [34]. The details like analytical properties, probabilistic interpretations, simulation algorithms estimation methods and applications are not given, because of the length of this paper.…”

A family of Gamma-generated distributions: Statistical properties and applications

“…Aslam et al. 25 proposed a new family of distributions, namely a modified T-X family of distributions with three most attractive features: flexibility, efficiency and parsimony.…”

A Novel Generalized Family of Distributions for Engineering and Life Sciences Data Applications

“…where v (z) is the PDF of any continuous random variable. Particularly, they derived subfamilies which include new Weibull-X family [10], logistic-X family [11], weighted T-X family [12], and modified T-X family [13].…”