Estimation of Parameters and Reliability Characteristics in Lindley Distribution Using Randomly Censored Data

This article deals with the estimation of parameters and reliability characteristics of Lindley distribution underrandom censoring. Expected time on test based on randomly censored data is obtained. The maximum likelihood estimators of the unknown parameters and reliability characteristics are derived. The asymptotic, bootstrap p and bootstrap t confidence intervals of the parameters are constructed. The Bayes estimators of the parameters and reliability characteristics under squared error loss function using non-informative and gamma informative priors are obtained. For computing of Bayes estimates, Lindley approximation and MCMC methods are considered. Highest posterior density (HPD) credible intervals of the parameters are obtained using MCMC method. Various estimation procedures are compared using a Monte Carlo simulation study. Finally, a real data set is analyzed for illustration purposes.

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Maximum Likelihood and Bayes Estimation in Randomly Censored Geometric Distribution

Journal of Probability and Statistics ◽

10.1155/2017/4860167 ◽

2017 ◽

Vol 2017 ◽

pp. 1-12

Author(s):

Hare Krishna ◽

Neha Goel

Keyword(s):

Maximum Likelihood ◽

Censored Data ◽

Geometric Distribution ◽

Information Matrix ◽

Bayes Estimation ◽

Data Set ◽

Monte Carlo Simulation Study ◽

Randomly Censored Data ◽

Highest Posterior Density ◽

Randomly Censored

In this article, we study the geometric distribution under randomly censored data. Maximum likelihood estimators and confidence intervals based on Fisher information matrix are derived for the unknown parameters with randomly censored data. Bayes estimators are also developed using beta priors under generalized entropy and LINEX loss functions. Also, Bayesian credible and highest posterior density (HPD) credible intervals are obtained for the parameters. Expected time on test and reliability characteristics are also analyzed in this article. To compare various estimates developed in the article, a Monte Carlo simulation study is carried out. Finally, for illustration purpose, a randomly censored real data set is discussed.

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Inferences for Weibull parameters under progressively first-failure censored data with binomial random removals

Statistics Optimization & Information Computing ◽

10.19139/soic-2310-5070-611 ◽

2020 ◽

Vol 9 (1) ◽

pp. 47-60

Author(s):

Samir K. Ashour ◽

Ahmed A. El-Sheikh ◽

Ahmed Elshahhat

Keyword(s):

Monte Carlo ◽

Censored Data ◽

Real Data ◽

Unknown Parameters ◽

Data Set ◽

Monte Carlo Simulation Study ◽

Squared Error Loss Function ◽

Bayes Estimates ◽

Monte Carlo Techniques ◽

Credible Intervals

In this paper, the Bayesian and non-Bayesian estimation of a two-parameter Weibull lifetime model in presence of progressive first-failure censored data with binomial random removals are considered. Based on the s-normal approximation to the asymptotic distribution of maximum likelihood estimators, two-sided approximate confidence intervals for the unknown parameters are constructed. Using gamma conjugate priors, several Bayes estimates and associated credible intervals are obtained relative to the squared error loss function. Proposed estimators cannot be expressed in closed forms and can be evaluated numerically by some suitable iterative procedure. A Bayesian approach is developed using Markov chain Monte Carlo techniques to generate samples from the posterior distributions and in turn computing the Bayes estimates and associated credible intervals. To analyze the performance of the proposed estimators, a Monte Carlo simulation study is conducted. Finally, a real data set is discussed for illustration purposes.

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