scholarly journals A Comparative Study of Maximum Likelihood Estimation and Bayesian Estimation for Erlang Distribution and Its Applications

2020 ◽  
Author(s):  
Kaisar Ahmad ◽  
Sheikh Parvaiz Ahmad
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Comparative Study ◽  
Bayesian Estimation ◽  
Likelihood Estimation ◽  
Erlang Distribution

scholarly journals Bayesian and Maximum Likelihood Estimation of the Shape Parameter of Exponential Inverse Exponential Distribution: A Comparative Approach

2020 ◽  
pp. 28-43
Author(s):  
Innocent Boyle Eraikhuemen ◽  
Fadimatu Bawuro Mohammed ◽  
Ahmed Askira Sule
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Bayesian Estimation ◽  
Exponential Distribution ◽  
Shape Parameter ◽  
Likelihood Estimation ◽  
Monte Carlo Study ◽  
Comparative Approach ◽  
The Mean ◽  
Inverse Exponential Distribution

This paper aims at making Bayesian analysis on the shape parameter of the exponential inverse exponential distribution using informative and non-informative priors. Bayesian estimation was carried out through a Monte Carlo study under 10,000 replications. To assess the effects of the assumed prior distributions and loss function on the Bayesian estimators, the mean square error has been used as a criterion. Overall, simulation results indicate that Bayesian estimation under QLF outperforms the maximum likelihood estimation and Bayesian estimation under alternative loss functions irrespective of the nature of the prior and the sample size. Also, for large sample sizes, all methods perform equally well.

scholarly journals Bayes Estimators for the Parameter of the Inverted Exponential Distribution Under different Double informative priors

2018 ◽  
Vol 24 (103) ◽  
pp. 18
Author(s):  
جنان عباس ناصر
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Exponential Distribution ◽  
Likelihood Estimation ◽  
Bayes Estimation ◽  
Erlang Distribution ◽  
Mean Square ◽  
Informative Priors ◽  
Chi Squared ◽  
Mean Square Errors

In this paper, we present a comparison of double informative priors which are assumed for the parameter of inverted exponential distribution.To estimate the parameter of inverted exponential distribution by using Bayes estimation ,will be  used two different kind of information in the Bayes estimation; two different priors have been selected for the parameter of inverted exponential distribution. Also assumed Chi-squared - Gamma distribution, Chi-squared - Erlang distribution, and- Gamma- Erlang distribution as double priors. The results are the derivations of these estimators under the squared error loss function with three different double priors. Additionally Maximum likelihood estimation method (MLE) was used  to estimate the parameter of inverted exponential distribution .We used simulation technique, to compare the performance for each estimator, several cases from inverted exponential distribution for data generating, for different samples sizes (small, medium, and large).Simulation results shown that the best method is the bayes  estimation according to the smallest values of mean square errors( MSE) for all samples sizes (n) comparative to the estimated values by using MLE . According to obtained results, we see that when the double prior distribution for  is Gamma- Erlang distribution for some values for the parameters a, b & given the best results according to the smallest values of mean square errors (MSE) comparative to the same values which obtained by using Maximum likelihood estimation (MLE) for the assuming true values for and for all samples sizes.  

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