scholarly journals Maximum Likelihood and Bayes Estimation in Randomly Censored Geometric Distribution

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.

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

2020 ◽  
Vol 8 (1) ◽  
pp. 80-97
Author(s):  
Renu Garg ◽  
Madhulika Dube ◽  
Hare Krishna
Keyword(s):  
Censored Data ◽  
Estimation Of Parameters ◽  
Data Set ◽  
Monte Carlo Simulation Study ◽  
Squared Error Loss Function ◽  
Lindley Distribution ◽  
Reliability Characteristics ◽  
Randomly Censored Data ◽  
Highest Posterior Density ◽  
Randomly Censored

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.

scholarly journals Statistical Inference of the Rayleigh Distribution Based on Progressively Type II Censored Competing Risks Data

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 898 ◽  
Author(s):  
Hongyi Liao ◽  
Wenhao Gui
Keyword(s):  
Competing Risks ◽  
Loss Function ◽  
Information Matrix ◽  
Real Life ◽  
Rayleigh Distribution ◽  
Bayes Estimation ◽  
Type Ii ◽  
Data Set ◽  
Squared Error Loss Function ◽  
Highest Posterior Density

A competing risks model under progressively type II censored data following the Rayleigh distribution is considered. We establish the maximum likelihood estimation for unknown parameters and compute the observed information matrix and the expected Fisher information matrix to construct the asymptotic confidence intervals. Moreover, we obtain the Bayes estimation based on symmetric and non-symmetric loss functions, that is, the squared error loss function and the general entropy loss function, and the highest posterior density intervals are also derived. In addition, a simulation study is presented to assess the performances of different methods discussed in this paper. A real-life data set analysis is provided for illustration purposes.

Estimation of P(X

2017 ◽  
Vol 34 (7) ◽  
pp. 1111-1122 ◽  
Author(s):  
Soumya Roy ◽  
Biswabrata Pradhan ◽  
E.V. Gijo
Keyword(s):  
Maximum Likelihood ◽  
Censored Data ◽  
Quality Characteristic ◽  
Logistic Distribution ◽  
Type Ii ◽  
Finite Sample ◽  
Data Set ◽  
Content Type ◽  
Type Ii Censored Data ◽  
Interval Estimators

Purpose The purpose of this paper is to compare various methods of estimation of P(X<Y) based on Type-II censored data, where X and Y represent a quality characteristic of interest for two groups. Design/methodology/approach This paper assumes that both X and Y are independently distributed generalized half logistic random variables. The maximum likelihood estimator and the uniformly minimum variance unbiased estimator of R are obtained based on Type-II censored data. An exact 95 percent maximum likelihood estimate-based confidence interval for R is also provided. Next, various Bayesian point and interval estimators are obtained using both the subjective and non-informative priors. A real life data set is analyzed for illustration. Findings The performance of various point and interval estimators is judged through a detailed simulation study. The finite sample properties of the estimators are found to be satisfactory. It is observed that the posterior mean marginally outperform other estimators with respect to the mean squared error even under the non-informative prior. Originality/value The proposed methodology can be used for comparing two groups with respect to a suitable quality characteristic of interest. It can also be applied for estimation of the stress-strength reliability, which is of particular interest to the reliability engineers.

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

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.

A Cramer-von Mises Statistic for Randomly Censored Data

Biometrika ◽  
1976 ◽  
Vol 63 (3) ◽  
pp. 465 ◽  
Author(s):  
James A. Koziol ◽  
Sylvan B. Green
Keyword(s):  
Censored Data ◽  
Von Mises Statistic ◽  
Von Mises ◽  
Randomly Censored Data ◽  
Randomly Censored ◽  
Cramer Von Mises
Sign in / Sign up

Export Citation Format

Share Document