Abstract
In this paper, we produced a new family of distribution called Gull Alpha Power Family of distributions (GAPF). A Special case of GAPF is derived by considering the Weibull distribution as a baseline distribution called Gull Alpha Power Weibull distribution (GAPW). The suitability of the proposed distribution derives from its ability to model both the monotonic and non-monotonic hazard rate functions which are a common practice in survival analysis and reliability engineering. Various statistical properties were derived in addition to their special cases. The unknown parameters of the model are estimated using the maximum likelihood method. Moreover, the usefulness of the proposed distribution is supported by using two real lifetime data sets as well as simulated data.
Highlights
From last few years, researchers made a contribution to the theory of probability so as to remove some of the limitations of the existing probability distributions
Al-Aqtash et al [1] produced a new family of distributions using the logit function and derived the special case named as Gumbel-Weibull distribution
Researchers have been constructing different modified versions of the Weibull distribution, for example, Almalki & Yuan [19] presented the New modified Weibull distribution, A new extension of Weibull distribution is presented by [20], a four parameter Weibull distribution is studied by Lemonte et al [21], Gumbel-Weibull distribution was explored by Al-Aqtash et al [22], Almheidat et al [23] investigated the generalized form of the Weibull distribution, Almalki & Nadarajah [24] by working with the discrete form of the Weibull distribution, and a flexible Weibull extension was introduced by Bebbington et al [25]
Summary
Researchers made a contribution to the theory of probability so as to remove some of the limitations of the existing probability distributions. This distribution fails to model a non-monotonic hazard rate function, for example, a failure rate of the electronic device, accident rate, and infant mortality rate To achieve this goal, researchers have been constructing different modified versions of the Weibull distribution, for example, Almalki & Yuan [19] presented the New modified Weibull distribution, A new extension of Weibull distribution is presented by [20], a four parameter Weibull distribution is studied by Lemonte et al [21], Gumbel-Weibull distribution was explored by Al-Aqtash et al [22], Almheidat et al [23] investigated the generalized form of the Weibull distribution, Almalki & Nadarajah [24] by working with the discrete form of the Weibull distribution, and a flexible Weibull extension was introduced by Bebbington et al [25]. The failure or hazard rate function of GAPW is defined as hGAPW ðyÞ f ðyÞ , 1À FðyÞ transforming Eqs (4) and (5), we obtain the result given below aeÀ byg bgygÀ 1eÀ byg À aeÀ byg logðaÞbgygÀ 1ð1 À eÀ byg ÞeÀ byg
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