The New Extended Flexible Weibull Distribution and Its Applications

Abstract

Abstract:The present article considers a new function to propose a new lifetime distribution. The new distribution is introduced by mixing up a linear system of the two logarithms of cumulative hazard functions. The proposed model is called new extended flexible Weibull distribution and is able to model lifetime with bathtub shaped failure rates and offers greater flexibility. Therefore, it can be quite valuable to use an alternative model to other existing lifetime distributions, where, modeling of real data sets with bathtub shaped failure rates are of interest. A brief description of the statistical properties along with estimation of the parameters through maximum likelihood procedure are discussed. The potentiality of the proposed model is showed by discussing two real data sets. For these data sets, the proposed model outclasses the Flexible Weibull Extension, Inverse Flexible Weibull Extension and Modified Weibull distributions.

A Study on Various Transformation Method of Weibull Distribution: A Review

“…The reliability function of the New Extended Flexible Weibull (NEx-FW) distribution [17] is given as, ( ) = ; > 0, , , > 0 and the corresponding hazard rate function is given as, ( ) = ( + 2 ) ; > 0, , , > 0 2.1.8.1 Shape behaviour of NEx-FW distribution BT shape hazard rate function, if > 1, < 1 and < 1…”

“…Over the years many generalization of the Weibull distribution have been studied by various researchers, the exponentiated Weibull distribution (Mudholkar & Srivastava [3]; Pal et al [4];Nassar et al [5];Mustafa et al [6]; Abdullah et al [7]), a review has been presented by Nadarajah et al, [8] on exponentiated Weibull distribution, extended Weibull distribution (Marshall & Olkin [9]), modified Weibull distribution (Xie et al [10]; Lai et al [11]; Sarhan et al [12]; Doostmoradi et al [13]; Almalki [14]), flexible Weibull extension (Bebbington et al [15]; Mustafa et al [6]; Mustafa et al [16]; Ahmad et al [17]; Ahmad et al [18]; park et al [19]) and the transformed Weibull distribution (Alzaatreh et al [20]). The hazard rate function of this distribution can be increasing, decreasing, bathtub shaped or unimodal.…”

Log - expo Transformation Flexible Weibull Three Parameter Distribution LET- FW

“…Proposed a general class of fexible Weibull distribution functions which in cludes some well-known modified Weibull distributions [15]. [21]. Zubair (2017).…”

A New Generalized- X Family for Analyzing the COVID-19 Data Set: a Case Study

“…Ahmad and Hussain [9] introduced a NEF-Weibull (new extended exible-Weibull) distribution to model the lifetime data with bathtub-shaped failure rates. Some other modi ed and extended distributions include the beta-Weibull (B-Weibull) distribution of Famoye et al [10]; the exible Weibull (FWEx) distribution of Bebbington et al [11]; the generalized modi ed Weibull (GM-Weibull) distribution proposed by Carrasco et al [12]; the Kumaraswamy Weibull (K-Weibull) distribution proposed by Cordeiro et al [13]; the beta modi ed Weibull (BM-Weibull) distribution of Silva et al [14]; the exponentiated modi ed Weibull extension (EMWE) distribution introduced by Sarhan and Apaloo [15]; the Gumbel-Lomax (GL) distribution suggested by Tahir et al [16]; and the Marshall-Olkin inverse Lomax distribution (MO-ILD) studied by Maxwell et al [17].…”