In this paper, the Weibull extension distribution parameters are estimated under a progressive type-II censoring scheme with random removal. The parameters of the model are estimated using the maximum likelihood method, maximum product spacing, and Bayesian estimation methods. In classical estimation (maximum likelihood method and maximum product spacing), we did use the Newton–Raphson algorithm. The Bayesian estimation is done using the Metropolis–Hastings algorithm based on the square error loss function. The proposed estimation methods are compared using Monte Carlo simulations under a progressive type-II censoring scheme. An empirical study using a real data set of transformer insulation and a simulation study is performed to validate the introduced methods of inference. Based on the result of our study, it can be concluded that the Bayesian method outperforms the maximum likelihood and maximum product-spacing methods for estimating the Weibull extension parameters under a progressive type-II censoring scheme in both simulation and empirical studies.
This research aims to model the COVID-19 in different countries, including Italy, Puerto Rico, and Singapore. Due to the great applicability of the discrete distributions in analyzing count data, we model a new novel discrete distribution by using the survival discretization method. Because of importance Marshall- Olkin family and the inverse Toppe-Leone distribution, both of them were used to introduce a new discrete distribution called Marshall–Olkin inverse Toppe-Leone distribution, this new distribution namely the new discrete distribution called discrete Marshall- Olkin Inverse Toppe-Leone (DMOITL). This new model posses only two parameters, also many properties have been obtained such as reliability measures and moment functions. The classical method as likelihood method and Bayesian estimation methods are applied to estimate the unknown parameters of DMOITL distributions. The Monte–Carlo simulation procedure is carried out to compare the maximum likelihood and Bayesian estimation methods. The highest posterior density (HPD) confidence intervals are used to discuss credible confidence intervals of parameters of new discrete distribution for the results of the Markov Chain Monte Carlo technique (MCMC).
This paper deals with the estimation of the parameters for asymmetric distribution and some lifetime indices such as reliability and hazard rate functions based on progressive first-failure censoring. Maximum likelihood, bootstrap and Bayesian approaches of the distribution parameters and reliability characteristics are investigated. Furthermore, the approximate confidence intervals and highest posterior density credible intervals of the parameters are constructed based on the asymptotic distribution of the maximum likelihood estimators and Markov chain Monte Carlo technique, respectively. In addition, the delta method is implemented to obtain the variances of the reliability and hazard functions. Moreover, we apply two methods of bootstrap to construct the confidence intervals. The Bayes inference based on the squared error and LINEX loss functions is obtained. Extensive simulation studies are conducted to evaluate the behavior of the proposed methods. Finally, a real data set of the COVID-19 mortality rate is analyzed to illustrate the estimation methods developed here.
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