Survival and Hazard Estimation of Weibull Distribution Based on Interval Censored Data

This paper describes the Maximum Likelihood Estimator and the Bayesian using gamma prior Estimator of the Weibull distribution based on interval censored data. The Bayesian estimates of the survival and hazard functions we can’t solve it analytical for that Gauss Quadrature method is used to estimate the survival and hazard functions. Also Lindley’s approximation is used. The two methods are compared to maximum likelihood counterparts and the comparisons are made with respect to the Mean Square Error (MSE) and absolute bias to determine the best for estimating of the survival and hazard function. Keywords: Weibull distribution, survival and hazard functions, Bayesian method, interval censored data, Gauss Quadrature, Lindley’s approximation

Maximum likelihood estimation of exponential distribution under type-ii censoring from imprecise data

Statistical analysis of lifetime distributions under Type-II censoring scheme is based on precise lifetime data. However, some collected lifetime data might be imprecise and are represented in the form of fuzzy numbers. This paper deals with the estimation of exponential mean parameter under Type-II censoring scheme when the lifetime observations are fuzzy and are assumed to be related to underlying crisp realization of a random sample. Maximum likelihood estimate of the unknown parameter is obtained by using EM algorithm. In addition, a new numerical method for parameter estimation is provided. Using the parametric bootstrap method, the construction of confidence intervals for the mean parameter is discussed. Monte Carlo simulations are performed to investigate performance of the different methods. Finally, an illustrative example is also included.Keywords: Type-II censoring, Imprecise lifetime, Exponential distribution, Maximumlikelihood estimation, Bootstrap confidence interva