Beta Exponentiated Modified Weibull Distribution: Properties and Application

Abstract

One of the most prominent statistical distributions is the Weibull distribution. The recent modifications in this distribution have enhanced its application but only in specific fields. To introduce a more generalized Weibull distribution, in this work beta exponentiated modified Weibull distribution is established. This distribution consolidate the exponential, skewed and symmetric shapes into one density. The proposed distribution also contains nineteen lifetime distributions as a special case, which shows the flexibility of the distribution. The statistical properties of the proposed model are derived and discussed, including reliability analysis and order statistics. The hazard function of the proposed distribution can have a unimodal, decreasing, bathtub, upside-down bathtub, and increasing shape that make it effective in reliability analysis. The parameters of the proposed model are evaluated by maximum likelihood and least squares estimation methods. The significance of the beta exponentiated modified Weibull distribution for modeling is illustrated by the study of real data. The numerical study indicates that the new proposed distribution gives better results than other comparable distributions.

Reliability Analysis for Electronic Devices Using Generalized Exponential Distribution

“…It is also preferred over the gamma and Weibull distributions [20] because the CDF of gamma distribution is not in a closed form while Weibull distribution does not accommodate monotonic hazard rate. It is worth mentioning that this distribution is a special case of the exponentiated Weibull distribution introduced by Mudholkar and Srivastava [23] and later on many distributions have developed using this idea [24]. Gupta and Kundu [25] presented some new and existing results for the generalized exponential distribution and discussed it suitability in different situations.…”

Beta-Exponentiated Ishita Distribution and Its Applications

“…Several other beta-generated class of distributions available in the literature are found in [9]- [38], among others.…”

The Exponentiated Truncated Inverse Weibull-Generated Family of Distributions with Applications

“…In this regard, we may refer to the unavoidable book by [22], as well as the survey by [23]. Then, several modifications and extensions have been proposed (see [23,24], and the references therein). The inverse Weibull (IW) distribution is one of these modifications, defined as the distribution of the reciprocal of a random variable following the standard W distribution.…”

“…We thus follow the spirit of the constructions of the odd generalized exponential-G (OGE-G) family by [29], exponentiated T-G (ET-G) family by [30], type II power Topp-Leone-G (TIIPL-G) family by [31] and exponentiated power generalized Weibull power series-G (EPGWPS-G) family by [32], among others. On the other side, recent statistical works exploiting the benefit of adding a shape parameter to existing distributions can be found in [24,33,34]. Motivated by the exponentiated perspective, this paper is devoted to the complete study of the ETIW-G family, including its applicability in a statistical setting.…”