scholarly journals Inference on in the Two-Parameter Weibull Model Based on Records

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Ayman Baklizi
Keyword(s):  
Mean Squared Error ◽  
Weibull Model ◽  
Record Values ◽  
Simulation Studies ◽  
Error Performance ◽  
Posterior Density ◽  
Likelihood Estimator ◽  
Squared Error ◽  
Highest Posterior Density ◽  
Two Parameter

We consider the stress-strength reliability based on record values from the Weibull distribution. The Bayes estimator based on squared error loss and the maximum likelihood estimator are derived and their bias and mean squared error performance are studied. Likelihood-based confidence intervals as well as some bootstrap intervals are developed. We derived also the highest posterior density interval. Simulation studies are conducted to investigate and compare the performance of the estimators and intervals.

Record-Based Estimators for Weibull Distribution

2014 ◽  
Vol 14 (07) ◽  
pp. 1450026 ◽  
Author(s):  
Mahdi Teimouri ◽  
Saralees Nadarajah
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Shape Parameter ◽  
Mean Squared Error ◽  
Likelihood Estimation ◽  
Record Values ◽  
Likelihood Estimator ◽  
Squared Error ◽  
Upper Record Values ◽  
Upper Record

Teimouri and Nadarajah [Statist. Methodol.13 (2013) 12–24] considered bias corrected maximum likelihood estimation of the Weibull distribution based on upper record values. Here, we propose an estimator for the Weibull shape parameter based on consecutive upper records. It is shown by simulations that the proposed estimator has less bias and less mean squared error than an estimator due to Soliman et al. [Comput. Statist. Data Anal.51 (2006) 2065–2077] based on all upper records. Also, the proposed estimator can be considered as a good competitor for the maximum likelihood estimator of the shape parameter based on complete data. This is proved by simulations and using a real dataset.

Inadmissibility of the Maximum Likelihood Estimator in the Presence of Prior Information

1970 ◽  
Vol 13 (3) ◽  
pp. 391-393 ◽  
Author(s):  
B. K. Kale
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Maximum Likelihood Estimator ◽  
Loss Function ◽  
Prior Information ◽  
Mean Squared Error ◽  
Closed Interval ◽  
Likelihood Estimator ◽  
Usual Estimator ◽  
Squared Error

Lehmann [1] in his lecture notes on estimation shows that for estimating the unknown mean of a normal distribution, N(θ, 1), the usual estimator is neither minimax nor admissible if it is known that θ belongs to a finite closed interval [a, b] and the loss function is squared error. It is shown that , the maximum likelihood estimator (MLE) of θ, has uniformly smaller mean squared error (MSE) than that of . It is natural to ask the question whether the MLE of θ in N(θ, 1) is admissible or not if it is known that θ ∊ [a, b]. The answer turns out to be negative and the purpose of this note is to present this result in a slightly generalized form.

scholarly journals Inverted Topp-Leone Distribution: Contribution to a Family of J-Shaped Frequency Functions in Presence of Random Censoring

2021 ◽  
Author(s):  
Hiba Zeyada Muhammed ◽  
Essam Abd Elsalam Muhammed
Keyword(s):  
Monte Carlo ◽  
Real Data ◽  
Posterior Density ◽  
Data Set ◽  
Bayes Estimates ◽  
Squared Error ◽  
Distribution Shape ◽  
Highest Posterior Density Intervals ◽  
Metropolis Hasting Algorithm ◽  
Highest Posterior Density

In this paper, Bayesian and non-Bayesian estimation of the inverted Topp-Leone distribution shape parameter are studied when the sample is complete and random censored. The maximum likelihood estimator (MLE) and Bayes estimator of the unknown parameter are proposed. The Bayes estimates (BEs) have been computed based on the squared error loss (SEL) function and using Markov Chain Monte Carlo (MCMC) techniques. The asymptotic, bootstrap (p,t), and highest posterior density intervals are computed. The Metropolis Hasting algorithm is proposed for Bayes estimates. Monte Carlo simulation is performed to compare the performances of the proposed methods and one real data set has been analyzed for illustrative purposes.

scholarly journals A New Ridge-Type Estimator for the Gamma Regression Model

Scientifica ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Adewale F. Lukman ◽  
Issam Dawoud ◽  
B. M. Golam Kibria ◽  
Zakariya Y. Algamal ◽  
Benedicta Aladeitan
Keyword(s):  
Biological Activity ◽  
Regression Model ◽  
Mean Squared Error ◽  
Real Life ◽  
Regression Parameter ◽  
Likelihood Estimator ◽  
Response Variable ◽  
Explanatory Variables ◽  
Squared Error ◽  
The Mean

The known linear regression model (LRM) is used mostly for modelling the QSAR relationship between the response variable (biological activity) and one or more physiochemical or structural properties which serve as the explanatory variables mainly when the distribution of the response variable is normal. The gamma regression model is employed often for a skewed dependent variable. The parameters in both models are estimated using the maximum likelihood estimator (MLE). However, the MLE becomes unstable in the presence of multicollinearity for both models. In this study, we propose a new estimator and suggest some biasing parameters to estimate the regression parameter for the gamma regression model when there is multicollinearity. A simulation study and a real-life application were performed for evaluating the estimators' performance via the mean squared error criterion. The results from simulation and the real-life application revealed that the proposed gamma estimator produced lower MSE values than other considered estimators.

scholarly journals Modified Robust Ridge M-Estimators in Two-Parameter Ridge Regression Model

2021 ◽  
Vol 2021 ◽  
pp. 1-24
Author(s):  
Seyab Yasin ◽  
Sultan Salem ◽  
Hamdi Ayed ◽  
Shahid Kamal ◽  
Muhammad Suhail ◽  
...  
Keyword(s):  
Ridge Regression ◽  
Mean Squared Error ◽  
Least Square ◽  
Ridge Estimator ◽  
Least Square Estimator ◽  
Squared Error ◽  
Joint Problem ◽  
Ridge Regression Estimator ◽  
Simulation Results ◽  
Two Parameter

The methods of two-parameter ridge and ordinary ridge regression are very sensitive to the presence of the joint problem of multicollinearity and outliers in the y-direction. To overcome this problem, modified robust ridge M-estimators are proposed. The new estimators are then compared with the existing ones by means of extensive Monte Carlo simulations. According to mean squared error (MSE) criterion, the new estimators outperform the least square estimator, ridge regression estimator, and two-parameter ridge estimator in many considered scenarios. Two numerical examples are also presented to illustrate the simulation results.

scholarly journals Modifying Two-Parameter Ridge Liu Estimator Based on Ridge Estimation

2019 ◽  
pp. 881-890
Author(s):  
Tarek Mahmoud Omara
Keyword(s):  
Simulation Study ◽  
Mean Squared Error ◽  
Error Matrix ◽  
Liu Estimator ◽  
Mean Squared Error Matrix ◽  
Ridge Estimation ◽  
Squared Error ◽  
The Mean ◽  
Two Parameter

In this paper, we introduce the new biased estimator to deal with the problem of multicollinearity. This estimator is considered a modification of Two-Parameter Ridge-Liu estimator based on ridge estimation. Furthermore, the superiority of the new estimator than Ridge, Liu and Two-Parameter Ridge-Liu estimator were discussed. We used the mean squared error matrix (MSEM) criterion to verify the superiority of the new estimate.  In addition to, we illustrated the performance of the new estimator at several factors through the simulation study.

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