Estimation of Inverse Weibull Distribution Under Type-I Hybrid Censoring

The hybrid censoring is a mixture of Type I and Type II censoring schemes. This paper presents the statistical inferences of the Inverse Weibull distribution when the data are Type-I hybrid censored. First we consider the maximum likelihood estimators of the unknown parameters. It is observed that the maximum likelihood estimators can not be obtained in closed form. We further obtain the Bayes estimators and the corresponding highest posterior density credible intervals of the unknown parameters under the assumption of independent gamma priors using the importance sampling procedure. We also compute the approximate Bayes estimators using Lindley's approximation technique. We have performed a simulation study and a real data analysis in order to compare the proposed Bayes estimators with the maximum likelihood estimators.Comment: This paper is under review in the Austrian Journal of Statistics and will likely be published ther

Doubly Censored Data from Two-Component Mixture of Inverse Weibull Distributions: Theory and Applications

Finite mixture distributions consist of a weighted sum of standard distributions and are a useful tool for reliability analysis of a heterogeneous population. They provide the necessary flexibility to model failure distributions of components with multiple failure models. The analysis of the mixture models under Bayesian framework has received sizable attention in the recent years. However, the Bayesian estimation of the mixture models under doubly censored samples has not yet been introduced in the literature. The main objective of this paper is to discuss the Bayes estimation of the inverse Weibull mixture distributions under doubly censoring. Different priors and loss functions were assumed for the posterior estimation. The performance of the different estimators has been compared in terms of posterior risks

Forecasting Remission Time of a Treatment Method for Leukemia as an Application to Statistical Inference Approach

In this paper, Weibull-Linear Exponential distribution (WLED) has been investigated whether being it is a well - fit distribution to a clinical real data. These data represent the duration of remission achieved by a certain drug used in the treatment of leukemia for a group of patients. The statistical inference approach is used to estimate the parameters of the WLED through the set of the fitted data. The estimated parameters are utilized to evaluate the survival and hazard functions and hence assessing the treatment method through forecasting the duration of remission times of patients. A two-sample prediction approach has been applied to obtain a predictive sample based on the Bayes estimates of the parameters. The statistical inference approach is applied to the case of censored data namely Type-II hybrid censoring scheme, which is common in clinical studies

Bayesian Estimation of the Parameters of Two-Component Mixture of Rayleigh Distribution under Doubly Censoring

Recently, the Bayesian analysis of the two-component mixture of lifetime models under singly type I censored samples was discussed. The Bayes estimation of the parameters of mixture of two Rayleigh distributions (MTRD) is developed under doubly censoring. Different informative priors, under squared error loss function and k-loss function, have been assumed for the posterior estimation. The performance of different estimators has been compared in terms of posterior risks by analyzing the simulated and real life data sets