scholarly journals LARGE Estimation of the stress-strength reliability of progressively censored inverted exponentiated Rayleigh distributions

2017 ◽  
Vol 13 (1) ◽  
pp. 49-76 ◽  
Author(s):  
Akram Kohansal
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Confidence Intervals ◽  
Scale Parameter ◽  
Sampling Technique ◽  
Credible Interval ◽  
Type Ii ◽  
Shape Parameters ◽  
Likelihood Estimator ◽  
Censored Samples

Abstract Based on progressively Type-II censored samples, this paper deals with the estimation of R = P(X < Y) when X and Y come from two independent inverted exponentiated rayleigh distributions with different shape parameters, but having the same scale parameter. The maximum likelihood estimator and UMVUE of R is obtained. Different confidence intervals are presented. The Bayes estimator of R and the corresponding credible interval using the Gibbs sampling technique are also proposed. Monte Carlo simulations are performed to compare the performances of the different methods. One illustrative example is provided to demonstrate the application of the proposed method.

scholarly journals Statistical Inference for the Inverted Scale Family under General Progressive Type-II Censoring

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 731
Author(s):  
Jing Gao ◽  
Kehan Bai ◽  
Wenhao Gui
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Monte Carlo Simulations ◽  
Maximum Likelihood Estimator ◽  
Confidence Intervals ◽  
Interval Estimation ◽  
Bayesian Estimator ◽  
Small Samples ◽  
Likelihood Estimator ◽  
Scale Family

Two estimation problems are studied based on the general progressively censored samples, and the distributions from the inverted scale family (ISF) are considered as prospective life distributions. One is the exact interval estimation for the unknown parameter θ , which is achieved by constructing the pivotal quantity. Through Monte Carlo simulations, the average 90 % and 95 % confidence intervals are obtained, and the validity of the above interval estimation is illustrated with a numerical example. The other is the estimation of R = P ( Y < X ) in the case of ISF. The maximum likelihood estimator (MLE) as well as approximate maximum likelihood estimator (AMLE) is obtained, together with the corresponding R-symmetric asymptotic confidence intervals. With Bootstrap methods, we also propose two R-asymmetric confidence intervals, which have a good performance for small samples. Furthermore, assuming the scale parameters follow independent gamma priors, the Bayesian estimator as well as the HPD credible interval of R is thus acquired. Finally, we make an evaluation on the effectiveness of the proposed estimations through Monte Carlo simulations and provide an illustrative example of two real datasets.

scholarly journals Reliability Inference for the Multicomponent System Based on Progressively Type II Censored Samples from Generalized Pareto Distributions

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1176
Author(s):  
Lauren Sauer ◽  
Yuhlong Lio ◽  
Tzong-Ru Tsai
Keyword(s):  
Maximum Likelihood ◽  
Confidence Interval ◽  
System Reliability ◽  
Bootstrap Method ◽  
Multicomponent System ◽  
Type Ii ◽  
Censored Samples ◽  
Generalized Pareto ◽  
Pareto Distributions ◽  
Generalized Pareto Distributions

In this paper, the reliability of a k-component system, in which all components are subject to common stress, is considered. The multicomponent system will continue to survive if at least s out of k components’ strength exceed the common stress. The system reliability is investigated by utilizing the maximum likelihood estimator based on progressively type II censored samples from generalized Pareto distributions. The confidence interval of the system reliability can be obtained by using asymptotic normality with Fisher information matrix or bootstrap method approximation. An intensive simulation study is conducted to evaluate the performance of maximum likelihood estimators of the model parameters and system reliability for a variety of cases. For the confidence interval of the system reliability, simulation results indicate the bootstrap method approximation outperforms over the asymptotic normality approximation in terms of coverage probability.

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