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.

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.

Estimators which are Uniformly Better than the James-Stein Estimator

1997 ◽  
Vol 47 (3-4) ◽  
pp. 167-180 ◽  
Author(s):  
Nabendu Pal ◽  
Jyh-Jiuan Lin
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Maximum Likelihood Estimator ◽  
Multivariate Normal Distribution ◽  
Multivariate Normal ◽  
Likelihood Estimator ◽  
Mean Estimation ◽  
Stein Estimator ◽  
Mean Vector ◽  
Better Than

Assume i.i.d. observations are available from a p-dimensional multivariate normal distribution with an unknown mean vector μ and an unknown p .d. diaper- . sion matrix ∑. Here we address the problem of mean estimation in a decision theoretic setup. It is well known that the unbiased as well as the maximum likelihood estimator of μ is inadmissible when p ≤ 3 and is dominated by the famous James-Stein estimator (JSE). There are a few estimators which are better than the JSE reported in the literature, but in this paper we derive wide classes of estimators uniformly better than the JSE. We use some of these estimators for further risk study.

scholarly journals On the Maximum Likelihood Estimation of Extreme Value Index Based on k-Record Values

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Abderrahim Louzaoui ◽  
Mohamed El Arrouchi
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Maximum Likelihood Estimator ◽  
Likelihood Estimation ◽  
Record Values ◽  
Extreme Value ◽  
Extreme Value Index ◽  
Likelihood Estimator ◽  
Consistent Solution ◽  
Strongly Consistent

In this paper, we study the existence and consistency of the maximum likelihood estimator of the extreme value index based on k-record values. Following the method used by Drees et al. (2004) and Zhou (2009), we prove that the likelihood equations, in terms of k-record values, eventually admit a strongly consistent solution without any restriction on the extreme value index, which is not the case in the aforementioned studies.

scholarly journals Estimation of P{X < Y} for gamma exponential model

2014 ◽  
Vol 24 (2) ◽  
pp. 283-291 ◽  
Author(s):  
Milan Jovanovic ◽  
Vesna Rajic
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Exponential Distribution ◽  
Asymptotic Distribution ◽  
Simulation Study ◽  
Random Variables ◽  
Exponential Model ◽  
Independent Random Variables ◽  
Likelihood Estimator

In this paper, we estimate probability P{X < Y} when X and Y are two independent random variables from gamma and exponential distribution, respectively. We obtain maximum likelihood estimator and its asymptotic distribution. We perform some simulation study.

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