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In this paper, we focus on Bayesian estimation of the parameters in the geometric process (GP) in which the first occurrence time of an event is assumed to have Weibull distribution. The Bayesian estimators are derived based on both symmetric (Squared Error) and asymmetric (General Entropy, LINEX) loss functions. Since the Bayesian estimators of unknown parameters cannot be obtained analytically, Lindley's approximation and the Markov Chain Monte Carlo (MCMC) methods are applied to compute the Bayesian estimates. Furthermore, by using the MCMC methods, credible intervals of the parameters are constructed. Maximum likelihood (ML) estimators are also derived for unknown parameters. The confidence intervals of the parameters are obtained based on an asymptotic distribution of ML estimators. Moreover, the performances of the proposed Bayesian estimators are compared with the corresponding ML, modified moment and modified maximum likelihood estimators through an extensive simulation study. Finally, analyses of two different real data sets are presented for illustrative purposes. [ABSTRACT FROM AUTHOR]

In this paper, based on hybrid censored sample from a two parameter exponentiated half logistic distribution, we consider the problem of estimating the unknown parameters using frequentist and Bayesian approaches. Expectation-Maximization, Lindley's approximation and Metropolis-Hastings algorithms are used for obtaining point estimators and corresponding confidence intervals for the shape and scale parameters involved in the underlying model. Data analyses involving the survival times of patients suffering from cancer diseases and treated radiotherapy and/or chemotherapy have been performed. Finally, numerical simulation study was conducted to assess the performances of the so developed methods and conclusions on our findings are reported. [ABSTRACT FROM AUTHOR]

Based on record statistics from three-parameter modified Weibull distribution, we consider the problem of estimating the unknown parameters using Bayesian and non-Bayesian approaches. Under a continuous-discrete joint prior distribution, Bayesian estimators and confidence intervals for the shape and scale parameters involved in the underlying model are obtained. In addition, maximum likelihood prediction and Bayesian prediction (either point or interval) of future record statistics based on an informative set of records are developed. Data analyses involving records extracted from a machine used to measure burr and times to breakdown of an insulating fluid between electrodes have been performed. Finally, Monte Carlo simulations are performed to compare the methods developed here. [ABSTRACT FROM AUTHOR]