Bayesian and maximum likelihood estimations of the inverse Weibull parameters under progressive type-II censoring

In this paper, the Weibull extension distribution parameters are estimated under a progressive type-II censoring scheme with random removal. The parameters of the model are estimated using the maximum likelihood method, maximum product spacing, and Bayesian estimation methods. In classical estimation (maximum likelihood method and maximum product spacing), we did use the Newton–Raphson algorithm. The Bayesian estimation is done using the Metropolis–Hastings algorithm based on the square error loss function. The proposed estimation methods are compared using Monte Carlo simulations under a progressive type-II censoring scheme. An empirical study using a real data set of transformer insulation and a simulation study is performed to validate the introduced methods of inference. Based on the result of our study, it can be concluded that the Bayesian method outperforms the maximum likelihood and maximum product-spacing methods for estimating the Weibull extension parameters under a progressive type-II censoring scheme in both simulation and empirical studies.

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Maximum Likelihood Estimation in Progressive Type-II Censoring

The Art of Progressive Censoring ◽

10.1007/978-0-8176-4807-7_12 ◽

2014 ◽

pp. 267-312

Author(s):

N. Balakrishnan ◽

Erhard Cramer

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Estimation ◽

Likelihood Estimation ◽

Type Ii ◽

Type Ii Censoring ◽

Progressive Type ◽

Progressive Type Ii Censoring

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Inference for the Two Parameter Reduced Kies Distribution under Progressive Type-II Censoring

Mathematics ◽

10.3390/math8111997 ◽

2020 ◽

Vol 8 (11) ◽

pp. 1997

Author(s):

Mansour Shrahili ◽

Naif Alotaibi ◽

Devendra Kumar ◽

Salem A. Alyami

Keyword(s):

Maximum Likelihood ◽

Estimation Methods ◽

Model Parameters ◽

Type Ii ◽

Type Ii Censoring ◽

Progressive Type ◽

Right Censored Order Statistics ◽

Censoring Scheme ◽

Two Parameter ◽

Progressive Type Ii Censoring

In this paper, we obtained several recurrence relations for the single and product moments under progressively Type-II right censored order statistics and then use these results to compute the means and variances of two parameter reduced Kies distribution. Besides, these moments are then utilized to derived best linear unbiased estimators of the scale and location parameters of two parameter reduced Kies distribution. The parameters of the two parameter reduced Kies distribution are estimated under progressive type-II censoring scheme. The model parameters are estimated using the maximum likelihood estimation method. Further, we explore the asymptotic confidence intervals for the model parameters. Monte Carlo simulations are performed to compare between the proposed estimation methods under progressive type-II censoring scheme. Based on our study, we can conclude that maximum likelihood estimators is decreasing with respect to an increase of the schemes and comparing the three censoring schemes, it is clear that the mean sum of squares, confidence interval lengths are smaller for scheme 1 than schemes 2 and 3.

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Progressive Type-II Censoring Schemes of Extended Odd Weibull Exponential Distribution with Applications in Medicine and Engineering

Mathematics ◽

10.3390/math8101679 ◽

2020 ◽

Vol 8 (10) ◽

pp. 1679

Author(s):

R. Alshenawy ◽

Ali Al-Alwan ◽

Ehab M. Almetwally ◽

Ahmed Z. Afify ◽

Hisham M. Almongy

Keyword(s):

Maximum Likelihood ◽

Exponential Distribution ◽

Confidence Intervals ◽

Estimation Methods ◽

Model Parameters ◽

Type Ii ◽

Type Ii Censoring ◽

Progressive Type ◽

Censoring Scheme ◽

Progressive Type Ii Censoring

In this paper, the parameters of the extended odd Weibull exponential distribution are estimated under progressive type-II censoring scheme with random removal. The model parameters are estimated using the maximum product spacing and maximum likelihood estimation methods. Further, we explore the asymptotic confidence intervals and bootstrap confidence intervals for the model parameters. Monte Carlo simulations are performed to compare between the proposed estimation methods under progressive type-II censoring scheme. An empirical study using two real datasets form engineering and medicine fields to validate the introduced methods of inference. Based on our study, we can conclude that the maximum product of spacing method outperforms the maximum likelihood method for estimating the extended odd Weibull exponential (EOWE) parameters under a progressive type-II censoring scheme in both numerical and empirical cases.

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