On the maximum-likelihood estimator for the location parameter of a cauchy distribution

1987 ◽  
Vol 15 (2) ◽  
pp. 137-146 ◽  
Author(s):  
Z. D. Bai ◽  
J. C. Fu
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Location Parameter ◽  
Cauchy Distribution ◽  
Likelihood Estimator

Estimating the Location Parameter of an Exponential Distribution with Known Coefficient of Variation

1982 ◽  
Vol 31 (3-4) ◽  
pp. 137-150 ◽  
Author(s):  
Malay Ghosh ◽  
Ahmad Razmpour
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Exponential Distribution ◽  
Coefficient Of Variation ◽  
Location Parameter ◽  
Likelihood Estimator ◽  
Scale Invariant

The plper considers estimation of the location parameter of an exponential distribution with known coefficient of variation. Several estimators including the maximum likelihood estimator and the best scale invariant estimator are proposed and compared.

scholarly journals Optimal Shrinkage Estimations for the Parameters of Exponential Distribution Based on Record Values

2016 ◽  
Vol 39 (1) ◽  
pp. 33-44 ◽  
Author(s):  
Hojatollah Zakerzadeh ◽  
Ali Akbar Jafari ◽  
Mahdieh Karimi
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Exponential Distribution ◽  
Location Parameter ◽  
Record Values ◽  
Shrinkage Estimator ◽  
Shrinkage Estimators ◽  
Likelihood Estimator ◽  
True Value ◽  
Better Than

<p>This paper studies shrinkage estimation after the preliminary test for the parameters of exponential distribution based on record values. The optimal value of shrinkage coefficients is also obtained based on the minimax regret criterion. The maximum likelihood, pre-test, and shrinkage estimators are compared using a simulation study. The results to estimate the scale parameter show that the optimal shrinkage estimator is better than the maximum likelihood estimator in all cases, and when the prior guess is near the true value, the pre-test estimator is better than shrinkage estimator. The results to estimate the location parameter show that the optimal shrinkage estimator is better than maximum likelihood estimator when a prior guess is close<br />to the true value. All estimators are illustrated by a numerical example.</p>

The Comparison Between the Bayes Estimator and the Maximum Likelihood Estimator of the Reliability Function for Negative Exponential Distribution

2018 ◽  
pp. 439
Author(s):  
Hazim Mansour Gorgees ◽  
Bushra Abdualrasool Ali ◽  
Raghad Ibrahim Kathum
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Exponential Distribution ◽  
Reliability Function ◽  
Bayes Estimator ◽  
Likelihood Estimator ◽  
Monte Carlo Simulation Technique ◽  
Negative Exponential Distribution ◽  
Negative Exponential ◽  
Better Than

     In this paper, the maximum likelihood estimator and the Bayes estimator of the reliability function for negative exponential distribution has been derived, then a Monte –Carlo simulation technique was employed to compare the performance of such estimators. The integral mean square error (IMSE) was used as a criterion for this comparison. The simulation results displayed that the Bayes estimator performed better than the maximum likelihood estimator for different samples sizes.

scholarly journals Transforming variables to central normality

2021 ◽  
Author(s):  
Jakob Raymaekers ◽  
Peter J. Rousseeuw
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Simulation Study ◽  
Real Data ◽  
Data Sets ◽  
Transformation Parameter ◽  
Likelihood Estimator ◽  
Extensive Simulation ◽  
Highly Sensitive

AbstractMany real data sets contain numerical features (variables) whose distribution is far from normal (Gaussian). Instead, their distribution is often skewed. In order to handle such data it is customary to preprocess the variables to make them more normal. The Box–Cox and Yeo–Johnson transformations are well-known tools for this. However, the standard maximum likelihood estimator of their transformation parameter is highly sensitive to outliers, and will often try to move outliers inward at the expense of the normality of the central part of the data. We propose a modification of these transformations as well as an estimator of the transformation parameter that is robust to outliers, so the transformed data can be approximately normal in the center and a few outliers may deviate from it. It compares favorably to existing techniques in an extensive simulation study and on real data.

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