Exponentiated generalized inverse Weibull distribution

Abstract

The inverse Weibull distribution can be readily applied to a wide range of situations including applications in medicine, reliability and ecology. In this article we introduce a new model of generalized inverse Weibull distribution referred to as the Exponentiated generalized inverse distribution. We provide a comprehensive mathematical treatment of this distribution. We derive the moment generating function and the rth moment thus generalizing some results in the literature. Expressions for the density, moment generating function and rth moment of the order statistics also are obtained. We discuss estimation of the parameters by maximum likelihood and provide the information matrix

The omega probability distribution and its applications in reliability theory

“…On the basis of this fact, several models were proposed to model bathtub‐shaped failure rates from the very beginning, which apply a variety of methods for estimating and testing including the method of moments, least squares, and maximum likelihood . Comprehensive overviews of bathtub‐shaped failure rate functions are provided by Rajarshi and Rajarshi and Lai et al Models that present bathtub‐shaped failure rates are also extremely useful in survival analysis . Much research has been carried out recently with the aim of serving the needs of reliability engineers and practitioners, most of them presenting new lifetime distributions that have bathtub‐shaped failure rate functions .…”

“…7,8,[10][11][12][13][14] Comprehensive overviews of bathtub-shaped failure rate functions are provided by Rajarshi and Rajarshi 8 and Lai et al 15 Models that present bathtub-shaped failure rates are also extremely useful in survival analysis. 16 Much research has been carried out recently with the aim of serving the needs of reliability engineers and practitioners, most of them presenting new lifetime distributions that have bathtub-shaped failure rate functions. 17 To satisfy all these needs, the Weibull distributions have also been proven to be very flexible in modeling various types of lifetime distributions.…”

Odds Generalized Exponential-Inverse Weibull Distribution: Properties & Estimation

“…Then, by using the exponential expansion for the last term in (6) and further the binomial expansion for a positive real power yields…”

“…Shahbaz et al (2012) suggested the Kumaraswamy inverse Weibull distribution. Elbatal and Muhammed (2014) introduced the exponentiated generalized inverse Weibull distribution. The generalized inverse Weibull distribution including the exponentiated or proportional reverse hazard and Kumaraswamy generalized inverse Weibull distributions have been suggested by Oluyede and Yang (2014).…”

The Exponentiated Generalized Standardized Half-logistic Distribution

“…We refer to the papers: Lemonte, A. J., 2014;Elbatal, I. & Muhammed, H. Z., 2014;Moors, 1988;Da Silva, et al, 2015;De Andrade, et al, 2015;Bourguignon, M., et al, 2015;Mansoor, M., et al, 2016;Arya, G.& Elbata, I., 2015 ;Silva, A. O., et al, 2015), which used the EG class to extend the Burr III, Birnbaum-Saunders, inverse Weibull, inverted exponential, generalized gamma, Gumbel, extended exponential, Fréchet, modified Weibull and Dagum distributions, respectively.…”