Exponentiated power generalized Weibull power series family of distributions: Properties, estimation and applications

Abstract

In this paper, we introduce the exponentiated power generalized Weibull power series (EPGWPS) family of distributions, obtained by compounding the exponentiated power generalized Weibull and power series distributions. By construction, the new family contains a myriad of new flexible lifetime distributions having strong physical interpretations (lifetime system, biological studies.. .). We discuss the characteristics and properties of the EPGWPS family, including its probability density and hazard rate functions, quantiles, moments, incomplete moments, skewness and kurtosis. The main vocation of the EPGWPS family remains to be applied in a statistical setting, and data analysis in particular. In this regard, we explore the estimation of the model parameters by the maximum likelihood method, with accuracy supported by a detailed simulation study. Then, we apply it to two practical data sets, showing the applicability and competitiveness of the EPGWPS models in comparison to some other well-reputed models.

Robust Assessment on the Developments of Three Extended Exponential Models with Some New Properties and Applications

“…Nascimento et al [92] and Reyad et al [93] introduced and studied ONH-G and NH-TL-G classes of distributions. Ahmad et al [94] proposed the odd DAL-G class, while Nasiru and Abubakari [95] and Aldahlan et al [96] proposed complementary generalized power Weibull power series and exponentiated power generalized Weibull power series families of distributions.…”

Box-Cox Gamma-G Family of Distributions: Theory and Applications

“…Statistical inference and applications of the BCG-HC model with parameters λ, δ and θ, as defined by the cdf in (18) or the pdf in (19), are explored in this section.…”

“…One of the most popular approaches to define such families is by using a so-called generator. In this regard, we refer the reader to the Marshall-Olkin-G family by [1], the exp-G family by [2], the beta-G family by [3], the gamma-G family by [4], the Kumaraswamy-G family by [5], the Ristić-Balakrishnan (RB)-G family (also called gamma-G type 2) by [6], the exponentiated generalized-G family by [7], the logistic-G family by [8], the transformerX (TX)-G family by [9], the Weibull-G family by [10], the exponentiated half-logistic-G family by [11], the odd generalized exponential-G family by [12], the odd Burr III-G family by [13], the cosine-sine-G family by [14], the generalized odd gamma-G family by [15], the extended odd-G family by [16], the type II general inverse exponential family by [17], the truncated Cauchy power-G family by [18], the exponentiated power generalized Weibull power series-G family by [19], the exponentiated truncated inverse Weibull-G family by [20], the ratio exponentiated general-G family by [21] and the Topp-Leone odd Fréchet-G family by [22].…”

Odd Inverse Power Generalized Weibull Generated Family of Distributions: Properties and Applications

“…Adding one or more form parameters results in these new generators, which improve accuracy and flexibility in modeling for a variety of diverse real-life applications. e most recent families of distributions to appear in the literature are as follows: a method for introducing a parameter into a family of distributions by [9], beta-G by [10], odd Nadarajah-Haghighi-G by [11], the odd Lindley-G by [12], and the odd Fréchet-G by [13], odd generalized exponential-G by [14], exponentiated power generalized Weibull power series family of distributions by [15], and odd generalized NH-G by [16], among others.…”