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http://dx.doi.org/10.5351/CSAM.2017.24.3.227

Inverted exponentiated Weibull distribution with applications to lifetime data  

Lee, Seunghyung (Department of Statistics, Pusan National University)
Noh, Yunhwan (Department of Statistics, Pusan National University)
Chung, Younshik (Department of Statistics, Pusan National University)
Publication Information
Communications for Statistical Applications and Methods / v.24, no.3, 2017 , pp. 227-240 More about this Journal
Abstract
In this paper, we introduce the inverted exponentiated Weibull (IEW) distribution which contains exponentiated inverted Weibull distribution, inverse Weibull (IW) distribution, and inverted exponentiated distribution as submodels. The proposed distribution is obtained by the inverse form of the exponentiated Weibull distribution. In particular, we explain that the proposed distribution can be interpreted by Marshall and Olkin's book (Lifetime Distributions: Structure of Non-parametric, Semiparametric, and Parametric Families, 2007, Springer) idea. We derive the cumulative distribution function and hazard function and calculate expression for its moment. The hazard function of the IEW distribution can be decreasing, increasing or bathtub-shaped. The maximum likelihood estimation (MLE) is obtained. Then we show the existence and uniqueness of MLE. We can also obtain the Bayesian estimation by using the Gibbs sampler with the Metropolis-Hastings algorithm. We also give applications with a simulated data set and two real data set to show the flexibility of the IEW distribution. Finally, conclusions are mentioned.
Keywords
Bayesian estimation; exponential inverted Weibull distribution; inverted exponentiated Weibull distribution; inverse Weibull distribution; Gibbs sampler; hazard function; maximum likelihood estimate; Metropolis-Hastings algorithm;
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