Bayesian and non-bayesian inference for logistic-exponential distribution using improved adaptive type-II progressively censored data.

Improved adaptive type-II progressive censoring schemes (IAT-II PCS) are increasingly being used to estimate parameters and reliability characteristics of lifetime distributions, leading to more accurate and reliable estimates. The logistic exponential distribution (LED), a flexible distribution with five hazard rate forms, is employed in several fields, including lifetime, financial, and environmental data. This research aims to enhance the accuracy and reliability estimation capabilities for the logistic exponential distribution under IAT-II PCS. By developing novel statistical inference methods, we can better understand the behavior of failure times, allow for more accurate decision-making, and improve the overall reliability of the model. In this research, we consider both classical and Bayesian techniques. The classical technique involves constructing maximum likelihood estimators of the model parameters and their asymptotic covariance matrix, followed by estimating the distribution's reliability using survival and hazard functions. The delta approach is used to create estimated confidence intervals for the model parameters. In the Bayesian technique, prior information about the LED parameters is used to estimate the posterior distribution of the parameters, which is derived using Bayes' theorem. The model's reliability is determined by computing the posterior predictive distribution of the survival or hazard functions. Extensive simulation studies and real-data applications assess the effectiveness of the proposed methods and evaluate their performance against existing methods.

Estimation and prediction for Burr type III distribution based on unified progressive hybrid censoring scheme.

The present communication develops the tools for estimation and prediction of the Burr-III distribution under unified progressive hybrid censoring scheme. The maximum likelihood estimates of model parameters are obtained. It is shown that the maximum likelihood estimates exist uniquely. Expectation maximization and stochastic expectation maximization methods are employed to compute the point estimates of unknown parameters. Based on the asymptotic distribution of the maximum likelihood estimators, approximate confidence intervals are proposed. In addition, the bootstrap confidence intervals are constructed. Furthermore, the Bayes estimates are derived with respect to squared error and LINEX loss functions. To compute the approximate Bayes estimates, Metropolis-Hastings algorithm is adopted. The highest posterior density credible intervals are obtained. Further, maximum a posteriori estimates of the model parameters are computed. The Bayesian predictive point, as well as interval estimates, are proposed. A Monte Carlo simulation study is employed in order to evaluate the performance of the proposed statistical procedures. Finally, two real data sets are considered and analysed to illustrate the methodologies established in this paper.