Abstract: The present paper deals with the maximum likelihood and Bayes estimation procedure for the shape and scale parameter of Poisson-exponential distribution for complete sample. Bayes estimators under symmetric and asymmetric loss function are obtained using Markov Chain Monte Carlo (MCMC) technique. Performances of the proposed Bayes estimators have been studied and compared with their maximum likelihood estimators on the basis of Monte Carlo study of simulated samples in terms of their risks. The methodology is also illustrated on a real data set.
In this paper, we proposed the Bayesian estimation for the parameter and reliability function of exponentiated gamma distribution under progressive type-II censored samples. The Bayes estimate of the parameter and reliability function are derived under the assumption of independent gamma prior by three different approximation methods namely Lindley’s approximation, Tierney-Kadane and Markov Chain Monte Carlo methods. Further, the comparison of Bayes estimators with corresponding maximum likelihood estimators have been carried out through simulation study. Finally, a real data set has been used to illustrate the above study in realistic phenomenon.
In this paper an attempt has been made to analyze the child mortality by use of a hazard model in Bayesian environment, family effect through multiplicative random effect is also incorporated in the model. For fitting this model real data has taken from District Level Household and Facility Survey (DLHS)-3. The largest state (in population) of India i.e. Uttar Pradesh data is taken for analysis. Deviance information criteria are used for comparison of models. It found that the model with family frailty gives better fit. All the analysis is performed in winBUGS software, which is used Markov chain monte carlo simulation under gibbs sampling.
Abstract: : In this paper, we discussed classical and Bayes estimation procedures for estimating the unknown parameters as well as the reliability and hazard functions of the flexible Weibull distribution when observed data are collected under progressively Type-II censoring scheme. The performances of the maximum likelihood and Bayes estimators are compared in terms of their mean squared errors through the simulation study. For the computation of Bayes estimates, we proposed the use of Lindley’s approximation and Markov Chain Monte Carlo (MCMC) techniques since the posteriors of the parameters are not analytically tractable. Further, we also derived the one and two sample posterior predictive densities of future samples and obtained the predictive bounds for future observations using MCMC techniques. To illustrate the discussed procedures, a set of real data is analysed.
Abstract: This paper aims to propose a suitable statistical model for the age distribution of prostate cancer detection. Descriptive studies suggest the onset of prostate cancer after 37 years of age with maximum diagnosis age at around 70 years. The major deficiency of descriptive studies is that the results cannot be generalized for all types of populations usually having non-identical environmental conditions. The proposition follows by checking the suitability of the model through different statistical tools like Akaike Information Criterion, Kolmogorov Smirnov distance, Bayesian Information Criterion and χ2 statistic. The Maximum likelihood estimate of the parameters of the proposed model along with their asymptotic confidence intervals have been obtained for the considered real data set.