scholarly journals On Progressive Type-II Censored Samples from Alpha Power Exponential Distribution

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Mukhtar M. Salah
Keyword(s):  
Exponential Distribution ◽  
Interval Estimation ◽  
Location Parameter ◽  
Alpha Power ◽  
Type Ii ◽  
Unknown Parameters ◽  
Progressive Type ◽  
Type Ii Censored Data ◽  
Best Linear Unbiased Estimators ◽  
Two Parameter

In this paper the two-parameter α -power exponential distribution is studied. We study the two-parameter α -power exponential μ , λ distribution with the location parameter μ > 0 and scale parameter λ > 0 under progressive Type-II censored data with fixed shape parameter α . We estimate the maximum likelihood estimators of these unknown parameters numerically since it cannot be solved analytically. We use the approximate best linear unbiased estimators μ ∗ and λ ∗ , as an initial guesses to obtain the MLEs μ ^ and λ ^ . We estimate the interval estimation of these unknowns’ parameters. Monte Carlo simulations are performed and data examples have been provided for illustration and comparison.

scholarly journals Statistical inferences for type-II hybrid censoring data from the alpha power exponential distribution

PLoS ONE ◽  
2021 ◽  
Vol 16 (1) ◽  
pp. e0244316
Author(s):  
Mukhtar M. Salah ◽  
Essam A. Ahmed ◽  
Ziyad A. Alhussain ◽  
Hanan Haj Ahmed ◽  
M. El-Morshedy ◽  
...  
Keyword(s):  
Exponential Distribution ◽  
Information Matrix ◽  
Expectation Maximization Algorithm ◽  
Location Parameter ◽  
Real Data ◽  
Estimation Methods ◽  
Invariance Property ◽  
Alpha Power ◽  
Type Ii ◽  
Hazard Functions

This paper describes a method for computing estimates for the location parameter μ > 0 and scale parameter λ > 0 with fixed shape parameter α of the alpha power exponential distribution (APED) under type-II hybrid censored (T-IIHC) samples. We compute the maximum likelihood estimations (MLEs) of (μ, λ) by applying the Newton-Raphson method (NRM) and expectation maximization algorithm (EMA). In addition, the estimate hazard functions and reliability are evaluated by applying the invariance property of MLEs. We calculate the Fisher information matrix (FIM) by applying the missing information rule, which is important in finding the asymptotic confidence interval. Finally, the different proposed estimation methods are compared in simulation studies. A simulation example and real data example are analyzed to illustrate our estimation methods.

scholarly journals Bayesian Estimation for Inverse Weibull Distribution Under Progressive Type-II Censored Data With Beta-Binomial Removals

2018 ◽  
Vol 47 (1) ◽  
pp. 77-94
Author(s):  
Pradeep Kumar Vishwakarma ◽  
Arun Kaushik ◽  
Aakriti Pandey ◽  
Umesh Singh ◽  
Sanjay Kumar Singh
Keyword(s):  
Weibull Distribution ◽  
Real Data ◽  
Estimation Procedure ◽  
Type Ii ◽  
Unknown Parameters ◽  
Data Set ◽  
Progressive Type ◽  
Inverse Weibull Distribution ◽  
Type Ii Censored Data ◽  
Censoring Scheme

This paper deals with the estimation procedure for inverse Weibull distribution under progressive type-II censored samples when removals follow Beta-binomial probability law. To estimate the unknown parameters, the maximum likelihood and Bayes estimators are obtained under progressive censoring scheme mentioned above. Bayes estimates are obtained using Markov chain Monte Carlo (MCMC) technique considering square error loss function and compared with the corresponding MLE's. Further, the expected total time on test is obtained under considered censoring scheme.  Finally, a real data set has been analysed to check the validity of the study.

scholarly journals Best Prediction Method for Progressive Type-II Censored Samples under New Pareto Model with Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Hanan Haj Ahmad
Keyword(s):  
Interval Estimation ◽  
Prediction Method ◽  
Estimation Methods ◽  
Type Ii ◽  
Unknown Parameters ◽  
Monte Carlo Techniques ◽  
Censored Samples ◽  
Pareto Model ◽  
Progressive Type ◽  
Mean Square Errors

This paper describes two prediction methods for predicting the non-observed (censored) units under progressive Type-II censored samples. The lifetimes under consideration are following a new two-parameter Pareto distribution. Furthermore, point and interval estimation of the unknown parameters of the new Pareto model is obtained. Maximum likelihood and Bayesian estimation methods are considered for that purpose. Since Bayes estimators cannot be expressed explicitly, Gibbs and the Markov Chain Monte Carlo techniques are utilized for Bayesian calculation. We use the posterior predictive density of the non-observed units to construct predictive intervals. A simulation study is performed to evaluate the performance of the estimators via mean square errors and biases and to obtain the best prediction method for the censored observation under progressive Type-II censoring scheme for different sample sizes and different censoring schemes.

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