Estimation methods in the presence of corner solutions

2019 ◽  
Vol 19 (1) ◽  
pp. 87-111 ◽  
Author(s):  
Alfonso Sánchez-Peñalver
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimators ◽  
Estimation Methods ◽  
Type Ii ◽  
Tobit Models ◽  
Corner Solution ◽  
Corner Solutions

In this article, I introduce a new command, nehurdle, that collects maximum likelihood estimators for linear, exponential, homoskedastic, and heteroskedastic tobit; truncated hurdle; and type II tobit models that involve explained variables with corner solutions. I review what a corner solution is as well as the assumptions of the mentioned models.

scholarly journals Shrinkage Estimators for the Exponential Scale Parameter under Multiply Type II Censoring

2016 ◽  
Vol 34 (1) ◽  
Author(s):  
Umesh Singh ◽  
Anil Kumar
Keyword(s):  
Maximum Likelihood ◽  
Exponential Distribution ◽  
Scale Parameter ◽  
Maximum Likelihood Estimators ◽  
Shrinkage Estimators ◽  
Type Ii ◽  
Approximate Maximum Likelihood ◽  
Type Ii Censoring ◽  
Mean Squared Errors

We consider the problem of estimating the scale parameter of an exponential distribution under multiply type II censoring when a prior point guess of the parameter value is available. Shrinkage estimators are obtained from the approximate maximum likelihood estimators proposed in Singh et al. (2004) and in Balasubramanian and Balakrishnan (1992). These estimators are then compared by their simulated mean squared errors.

scholarly journals E-Bayesian Estimation Based on Burr-X Generalized Type-II Hybrid Censored Data

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 626
Author(s):  
Abdalla Rabie ◽  
Junping Li
Keyword(s):  
Maximum Likelihood ◽  
Bayesian Estimation ◽  
Real Life ◽  
Estimation Method ◽  
Reliability Function ◽  
Maximum Likelihood Estimates ◽  
Estimation Methods ◽  
Type Ii ◽  
Credible Intervals ◽  
Generalized Type

In this article, we are concerned with the E-Bayesian (the expectation of Bayesian estimate) method, the maximum likelihood and the Bayesian estimation methods of the shape parameter, and the reliability function of one-parameter Burr-X distribution. A hybrid generalized Type-II censored sample from one-parameter Burr-X distribution is considered. The Bayesian and E-Bayesian approaches are studied under squared error and LINEX loss functions by using the Markov chain Monte Carlo method. Confidence intervals for maximum likelihood estimates, as well as credible intervals for the E-Bayesian and Bayesian estimates, are constructed. Furthermore, an example of real-life data is presented for the sake of the illustration. Finally, the performance of the E-Bayesian estimation method is studied then compared with the performance of the Bayesian and maximum likelihood methods.

scholarly journals Applying Transformer Insulation Using Weibull Extended Distribution Based on Progressive Censoring Scheme

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 100
Author(s):  
Hisham M. Almongy ◽  
Fatma Y. Alshenawy ◽  
Ehab M. Almetwally ◽  
Doaa A. Abdo
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Type Ii ◽  
Type Ii Censoring ◽  
Progressive Type ◽  
Transformer Insulation ◽  
Censoring Scheme ◽  
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.

scholarly journals Reliability estimation and parameter estimation for inverse Weibull distribution under different loss functions

2021 ◽  
Vol 49 (1) ◽  
Author(s):  
Asuman Yilmaz ◽  
◽  
Mahmut Kara ◽  
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Maximum Likelihood Estimators ◽  
Loss Functions ◽  
Estimation Methods ◽  
Mcmc Methods ◽  
Inverse Weibull Distribution ◽  
Mean Square Errors ◽  
Bayesian Estimators

In this paper, the classical and Bayesian estimators of the unknown parameters and the reliability function of the inverse Weibull distribution are considered. The maximum likelihood estimators (MLEs) and modified maximum likelihood estimators (MMLEs) are used in the classical parameter estimation. Bayesian estimators of the parameters are obtained by using symmetric and asymmetric loss functions under informative and non-informative priors. Bayesian computations are derived by using Lindley approximation and Markov chain Monte Carlo (MCMC) methods. The asymptotic confidence intervals are constructed based on the maximum likelihood estimators. The Bayesian credible intervals of the parameters are obtained by using the MCMC method. Furthermore, the performances of these estimation methods are compared concerning their biases and mean square errors through a simulation study. It is seen that the Bayes estimators perform better than the classical estimators. Finally, two real-life examples are given for illustrative purposes.

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

Mathematics ◽  
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.

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

Mathematics ◽  
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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