Bayesian Approach for estimating the unknown Scale parameter of Erlang Distribution Based on General Entropy Loss Function
We are used Bayes estimators for unknown scale parameter when shape Parameter is known of Erlang distribution. Assuming different informative priors for unknown scale parameter. We derived The posterior density with posterior mean and posterior variance using different informative priors for unk...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Baghdad
2023-07-01
|
| Series: | Ibn Al-Haitham Journal for Pure and Applied Sciences |
| Subjects: | |
| Online Access: | https://jih.uobaghdad.edu.iq/index.php/j/article/view/3099 |
| _version_ | 1797776213293400064 |
|---|---|
| author | Jinan A. Naser Al-obedy |
| author_facet | Jinan A. Naser Al-obedy |
| author_sort | Jinan A. Naser Al-obedy |
| collection | DOAJ |
| description |
We are used Bayes estimators for unknown scale parameter when shape Parameter is known of Erlang distribution. Assuming different informative priors for unknown scale parameter. We derived The posterior density with posterior mean and posterior variance using different informative priors for unknown scale parameter which are the inverse exponential distribution, the inverse chi-square distribution, the inverse Gamma distribution, and the standard Levy distribution as prior. And we derived Bayes estimators based on the general entropy loss function (GELF) is used the Simulation method to obtain the results. we generated different cases for the parameters of the Erlang model, for different sample sizes. The estimates have been compared in terms of their mean-squared error (MSE). We concluded that the best estimators of the scale parameterof the Erlang distribution, based on GELF for the shape parameter (c=1,2,3) under inverse gamma prior with for all samples sizes(n) where the true cases of the Erlang model are and according to the smallest values of MSE
|
| first_indexed | 2024-03-12T22:46:44Z |
| format | Article |
| id | doaj.art-ff7ec8dc777848e296d1696b2d6a5d2f |
| institution | Directory Open Access Journal |
| issn | 1609-4042 2521-3407 |
| language | English |
| last_indexed | 2024-03-12T22:46:44Z |
| publishDate | 2023-07-01 |
| publisher | University of Baghdad |
| record_format | Article |
| series | Ibn Al-Haitham Journal for Pure and Applied Sciences |
| spelling | doaj.art-ff7ec8dc777848e296d1696b2d6a5d2f2023-07-21T05:07:05ZengUniversity of BaghdadIbn Al-Haitham Journal for Pure and Applied Sciences1609-40422521-34072023-07-0136310.30526/36.3.3099Bayesian Approach for estimating the unknown Scale parameter of Erlang Distribution Based on General Entropy Loss FunctionJinan A. Naser Al-obedy0Technical College of Management-Baghdad, Middle Technical university, We are used Bayes estimators for unknown scale parameter when shape Parameter is known of Erlang distribution. Assuming different informative priors for unknown scale parameter. We derived The posterior density with posterior mean and posterior variance using different informative priors for unknown scale parameter which are the inverse exponential distribution, the inverse chi-square distribution, the inverse Gamma distribution, and the standard Levy distribution as prior. And we derived Bayes estimators based on the general entropy loss function (GELF) is used the Simulation method to obtain the results. we generated different cases for the parameters of the Erlang model, for different sample sizes. The estimates have been compared in terms of their mean-squared error (MSE). We concluded that the best estimators of the scale parameterof the Erlang distribution, based on GELF for the shape parameter (c=1,2,3) under inverse gamma prior with for all samples sizes(n) where the true cases of the Erlang model are and according to the smallest values of MSE https://jih.uobaghdad.edu.iq/index.php/j/article/view/3099The Erlang distribution, Bayes estimation, The posterior density, Posterior mean, Posterior variance, GELF, MSE. |
| spellingShingle | Jinan A. Naser Al-obedy Bayesian Approach for estimating the unknown Scale parameter of Erlang Distribution Based on General Entropy Loss Function Ibn Al-Haitham Journal for Pure and Applied Sciences The Erlang distribution, Bayes estimation, The posterior density, Posterior mean, Posterior variance, GELF, MSE. |
| title | Bayesian Approach for estimating the unknown Scale parameter of Erlang Distribution Based on General Entropy Loss Function |
| title_full | Bayesian Approach for estimating the unknown Scale parameter of Erlang Distribution Based on General Entropy Loss Function |
| title_fullStr | Bayesian Approach for estimating the unknown Scale parameter of Erlang Distribution Based on General Entropy Loss Function |
| title_full_unstemmed | Bayesian Approach for estimating the unknown Scale parameter of Erlang Distribution Based on General Entropy Loss Function |
| title_short | Bayesian Approach for estimating the unknown Scale parameter of Erlang Distribution Based on General Entropy Loss Function |
| title_sort | bayesian approach for estimating the unknown scale parameter of erlang distribution based on general entropy loss function |
| topic | The Erlang distribution, Bayes estimation, The posterior density, Posterior mean, Posterior variance, GELF, MSE. |
| url | https://jih.uobaghdad.edu.iq/index.php/j/article/view/3099 |
| work_keys_str_mv | AT jinananaseralobedy bayesianapproachforestimatingtheunknownscaleparameteroferlangdistributionbasedongeneralentropylossfunction |