A new alpha power transformed family of distributions: properties and applications to the Weibull model

Abstract

In this article, a new technique of alpha-power transformation is used to propose a new class of lifetime distributions. Four special models of the new family are presented. Some mathematical properties of the proposed model including estimation of the unknown parameters using the method of maximum likelihood are discussed. For the illustrative purposes of the new proposal, a three-parameter special model of this class, namely, new alpha-power transformed Weibull distribution is considered in detail. The proposed distribution offers greater distributional flexibility and is able to model data with increasing, decreasing, and constant or more importantly with bathtub-shaped failure rates. Type-1 and Type-II censoring estimation are discussed. A simulation study based on complete sample of the new model is also carried out. Finally, the usefulness and efficiency of the new proposal is illustrated by analyzing two real data sets.

The inverse Weibull inverse exponential distribution with application

“…The quantile function of the IWIE can be generated by inverting cdf (3) as 22 Maha A. Aldahlan (5) where U a uniform variate in the unit interval (0,1 ). The median can be calculated by inserting 0.5 u  in (5). Then, the median (M) is given by…”

“…In the recent years, many researchers are interested to expand generating family in order to obtain better fit for data analyzing. Some popular-known generating family are: The the beta-G by Eugene et al (2002), odd Frechet-G proposed by Haq and Elgarhy (2018), Muth-G studied by Almarashi and Elgarhy (2018), Elbatal et al (2018) proposed a new alpha power transformation family of distributions, Hassan and Nassr (2018) introduced inverse Weibull-G (IW-G) among others. The cdf and pdf of IW-G is (1) where G(.)…”

Marshall Olkin Alpha Power Extended Weibull Distribution: Different Methods of Estimation based on Type I and Type II Censoring

“…For example, [8] introduced alpha power Weibull (APW) distribution, [9] introduced new AP transformed family of distributions, [10,11] introduced AP transformed Lindley and inverse Lindley respectively, [12] introduced AP transformed power Lindley distribution and [13] introduced AP inverse Weibull distribution, have done a lot of works on distributions based on AP transformation.…”

Sine Topp-Leone-G family of distributions: Theory and applications

“…Then, the possible values of the new parameter(s) can significantly improve the statistical capabilities of the parent distribution, positively affecting the central and dispersion parameters, asymmetry, kurtosis and weight on the tails. Examples of such families are the exp-G family [35], Weibull-G family [20], Topp-Leone generated (TL-G) family [11], a new extended alpha power transformed-G [6], a new alpha power transformed-G [29], new power TL-G [17], type II general inverse exponential-G [40], truncated inverted Kumaraswamy-G [16], exponentiated truncated inverse Weibull-G [14], odd generalized NH-G [5], type II power TL-G [18] and others.…”