Generalized Transmuted Family of Distributions: Properties and Applications

Abstract

We introduce and study general mathematical properties of a new generator of continuous distributions with two extra parameters called the Generalized Transmuted Family of Distributions. We investigate the shapes and present some special models. The new density function can be expressed as a linear combination of exponentiated densities in terms of the same baseline distribution. We obtain explicit expressions for the ordinary and incomplete moments and generating function, Bonferroni and Lorenz curves, asymptotic distribution of the extreme values, Shannon and Rényi entropies and order statistics, which hold for any baseline model. Further, we introduce a bivariate extension of the new family. We discuss the different methods of estimation of the model parameters and illustrate the potential application of the model via real data. A brief simulation for evaluating Maximum likelihood estimator is done. Finally certain characterziations of our model are presented.

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

“…The mean of the MT-X family can be obtained by putting n = 1 in (11). Similarly, the higher order moments can be quantified by substituting n = 2, 3, .…”

“…The first data set from health surveillance comprises 128 patients and provides remission times (months) of bladder cancer, see Almheidat et al [22]. Also, the second data comprehends the lifetime data of 76 observations representing the life of fatigue fracture of Kevlar 373/epoxy, see Abdul-Moniem and Seham [23] and Alizadeh et al [11]. Both data sets are provided in the Appendix.…”

“…In persuasion, Alzaatreh et al [10] proposed an operator namely T-X family, capable of generating the mentioned families of distributions under certain specifications. For more recent development, one may see Alizadeh et al [11], Nofal et al [12], Cordeiro et al [13], Mahdavi and Kundu [14], Haq et al [15] and Basheer [16], among others. In this article, we focus on proposing a new family of distributions, namely modified T-X family of distributions.…”

Cubic Transmuted Uniform Distribution: An Alternative to Beta and Kumaraswamy Distributions

“…The proposed family of distributions provides the base distribution for λ = 0. The proposed cubic transmuted family given in (2) can be obtain as the distribution of order statistics and as a member of T − X family of distributions. We will obtain the propose family as distribution of order statistics and as a member of T − X family in the following theorems.…”

A New Four-ParameterWeibull Model for Lifetime Data

“…If λ = 0 and b = 1, the TExG-G model reduces to the exponentiated-G (Ex-G) family pioneered by Gupta et al (1998). If a = 1, it gives the transmuted generalized class (TG-G) defined by Alizadeh et al (2015) and, finally, the TExG-G model reduces to the baseline distribution when a = b = 1 and λ = 0. This paper is outlined as follows.…”