Bayesian and Non-Bayesian Estimation for the Bivariate Inverse Weibull Distribution Under Progressive Type-II Censoring
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Bayesian and Non-Bayesian Estimation for the Bivariate Inverse Weibull Distribution Under Progressive Type-II Censoring Hiba Z. Muhammed1 · Ehab M. Almetwally2 Received: 12 July 2020 / Revised: 10 October 2020 / Accepted: 20 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Recently, bivariate inverse Weibull distribution was derived; many of its properties have been discussed. Progressive Type-II censoring for bivariate inverse Weibull distribution has been proposed. The problem of estimating the unknown parameters of this distribution in the presence of progressive Type-II censoring by both Maximum likelihood and Bayesian estimation methods is considered in this paper. Moreover, asymptotic and bootstrap confidence intervals for the model parameters are obtained. Simulation study and a real data set are presented to illustrate the proposed procedure. Keywords Bivariate inverse Weibull distribution · Maximum likelihood estimation · Prior distribution · Bayesian estimation · Progressive Type-II censoring · Bootstrap confidence Intervals
1 Introduction Many times, the life failure data of interest is bivariate in nature. Any study on twins or on failure data recoded twice on the same system naturally leads to bivariate data. For example, Hougaard et al. [1] studied data on life length of Danish twins and Lin et al. [2] considered a data of colon cancer and the time from treatment to death. Paired data could consist of blindness in the left right eye, failure time of the left right kidney or age at death of parent/child in a genetic study. Eliwa and El-Morshedy [3] proposed
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Ehab M. Almetwally [email protected] Hiba Z. Muhammed [email protected]
1
Department of Mathematical Statistics, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, Egypt
2
Department of Statistics, Faculty of Business Administration, Delta University of Science and Technology, Mansoura, Egypt
123
Annals of Data Science
the bivariate Gumbel-G family, and they discussed Bayesian and maximum likelihood techniques to estimate parameters of this model. Almetwally et al. [4] introduced Farlie–Gumbel–Morgenstern (FGM) bivariate Weibull distribution, and they discussed maximum likelihood, inference function for margins and semi-parametric methods to estimate parameters of this model. Parameter estimation of bivariate Fréchet distribution based on Farlie–Gumbel–Morgenstern and Ali–Mikhail–Haq copulas has been introduced by Almetwally and Muhammed [5]. Yousaf et al. [6] discussed Bayesian and classical inferences for the Chen distribution assuming upper record values. Sultana et al. [7] investigated the estimation problems of the unknown parameters of the Kumaraswamy distribution under type I progressive hybrid censoring. El-Sherpieny et al. [8] obtained progressive Type-II hybrid censored samples based on maximum product spacing and maximum likelihood estimation method for power Lomax distribution. Almetwally et al. [9] discussed adaptive type-II progressive censoring schemes
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