Journal of Data Science

Abstract: The concept of frailty provides a suitable way to introduce random effects in the model to account for association and unobserved heterogeneity. In its simplest form, a frailty is an unobserved random factor that modifies multiplicatively the hazard function of an individual or a group or cluster of individuals. In this paper, we study positive stable distribution as frailty distribution and two different baseline distributions namely Pareto and linear failure rate distribution. We estimate parameters of proposed models by introducing Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique. In the present study a simulation is done to compare the true values of parameters with the estimated value. We try to fit the proposed models to a real life bivariate survival data set of McGrilchrist and Aisbett (1991) related to kidney infection. Also, we present a comparison study for the same data by using model selection criterion, and suggest a better model.

This article discusses the estimation of the Generalized Power Weibull parameters using the maximum product spacing (MPS) method, the maximum likelihood (ML) method and Bayesian estimation method under squares error for loss function. The estimation is done under progressive type-II censored samples and a comparative study among the three methods is made using Monte Carlo Simulation. Markov chain Monte Carlo (MCMC) method has been employed to compute the Bayes estimators of the Generalized Power Weibull distribution. The optimal censoring scheme has been suggested using two different optimality criteria (mean squared of error, Bias and relative efficiency). A real data is used to study the performance of the estimation process under this optimal scheme in practice for illustrative purposes. Finally, we discuss a method of obtaining the optimal censoring scheme.

In this paper, maximum likelihood and Bayesian methods of estimation are used to estimate the unknown parameters of two Weibull populations with the same shape parameter under joint progressive Type-I (JPT-I) censoring scheme. Bayes estimates of the parameters are obtained based on squared error and LINEX loss functions under the assumption of independent gamma priors. We propose to apply Markov Chain Monte Carlo (MCMC) technique to carry out a Bayesian estimation procedure. The approximate confidence intervals and the credible intervals for the unknown parameters are also obtained. Finally, we analyze a one real data set for illustration purpose.

In this work, we study the odd Lindley Burr XII model initially introduced by Silva et al. [29]. This model has the advantage of being capable of modeling various shapes of aging and failure criteria. Some of its statistical structural properties including ordinary and incomplete moments, quantile and generating function and order statistics are derived. The odd Lindley Burr XII density can be expressed as a simple linear mixture of BurrXII densities. Useful characterizations are presented. The maximum likelihood method is used to estimate the model parameters. Simulation results to assess the performance of the maximum likelihood estimators are discussed. We prove empirically the importance and flexibility of the new model in modeling various types of data. Bayesian estimation is performed by obtaining the posterior marginal distributions as well as using the simulation method of Markov Chain Monte Carlo (MCMC) by the Metropolis-Hastings algorithm in each step of Gibbs algorithm. The trace plots and estimated conditional posterior distributions are also presented.

Abstract: This article concerns the Bayesian estimation of interest rate mod els based on Euler-Maruyama approximation. Assume the short term inter est rate follows the CIR model, an iterative method of Bayesian estimation is proposed. Markov Chain Monte Carlo simulation based on Gibbs sam pler is used for the posterior estimation of the parameters. The maximum A-posteriori estimation using the genetic algorithm is employed for finding the Bayesian estimates of the parameters. The method and the algorithm are calibrated with the historical data of US Treasury bills.