Bayesian Estimation of Shift Point in Shape Parameter of Inverse Gaussian Distribution Under Different Loss Functions
In this paper, a Bayesian approach is proposed for shift point detection in an inverse Gaussian distribution. In this study, the mean parameter of inverse Gaussian distribution is assumed to be constant and shift points in shape parameter is considered. First the posterior distribution of shape para...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Islamic Azad University, Qazvin Branch
2015-07-01
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| Series: | Journal of Optimization in Industrial Engineering |
| Subjects: | |
| Online Access: | http://www.qjie.ir/article_216_0e38aaddfc4c867549097412e3c72196.pdf |
| _version_ | 1818651652164419584 |
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| author | Mohammad Saber Fallah Nezhad Batul Rasti |
| author_facet | Mohammad Saber Fallah Nezhad Batul Rasti |
| author_sort | Mohammad Saber Fallah Nezhad |
| collection | DOAJ |
| description | In this paper, a Bayesian approach is proposed for shift point detection in an inverse Gaussian distribution. In this study, the mean parameter of inverse Gaussian distribution is assumed to be constant and shift points in shape parameter is considered. First the posterior distribution of shape parameter is obtained. Then the Bayes estimators are derived under a class of priors and using various loss functions. We assumed uniform, Jeffreys, exponential, gamma and chi square distributions as prior distributions. The squared error loss function (SELF), entropy loss function (ELF), linex loss function (LLF) and precautionary loss function (PLF), are used as loss functions. We attempt to find out the best estimator for shift point under various priors and loss functions. The proposed Bayesian approach can be adapted to any similar problem for shift point detection. Simulation studies were done to investigate the performance of different loss functions. The results of simulation study denote that the Jeffrey prior distribution under PLF has the most accurate estimation of shift point for sample size of 20, and the gamma prior distribution under SELF has the most accurate estimation of shift point for sample size of 50. |
| first_indexed | 2024-12-17T02:09:31Z |
| format | Article |
| id | doaj.art-3419d82185dd4353a2f68b64066e958b |
| institution | Directory Open Access Journal |
| issn | 2251-9904 2423-3935 |
| language | English |
| last_indexed | 2024-12-17T02:09:31Z |
| publishDate | 2015-07-01 |
| publisher | Islamic Azad University, Qazvin Branch |
| record_format | Article |
| series | Journal of Optimization in Industrial Engineering |
| spelling | doaj.art-3419d82185dd4353a2f68b64066e958b2022-12-21T22:07:36ZengIslamic Azad University, Qazvin BranchJournal of Optimization in Industrial Engineering2251-99042423-39352015-07-01818112216Bayesian Estimation of Shift Point in Shape Parameter of Inverse Gaussian Distribution Under Different Loss FunctionsMohammad Saber Fallah Nezhad0Batul Rasti1Department of Industrial Engineering, Yazd University, Yazd, IranDepartment of Industrial Engineering, Yazd University, Yazd, IranIn this paper, a Bayesian approach is proposed for shift point detection in an inverse Gaussian distribution. In this study, the mean parameter of inverse Gaussian distribution is assumed to be constant and shift points in shape parameter is considered. First the posterior distribution of shape parameter is obtained. Then the Bayes estimators are derived under a class of priors and using various loss functions. We assumed uniform, Jeffreys, exponential, gamma and chi square distributions as prior distributions. The squared error loss function (SELF), entropy loss function (ELF), linex loss function (LLF) and precautionary loss function (PLF), are used as loss functions. We attempt to find out the best estimator for shift point under various priors and loss functions. The proposed Bayesian approach can be adapted to any similar problem for shift point detection. Simulation studies were done to investigate the performance of different loss functions. The results of simulation study denote that the Jeffrey prior distribution under PLF has the most accurate estimation of shift point for sample size of 20, and the gamma prior distribution under SELF has the most accurate estimation of shift point for sample size of 50.http://www.qjie.ir/article_216_0e38aaddfc4c867549097412e3c72196.pdfBayes estimatorsshift pointinverse Gaussian distributionloss function |
| spellingShingle | Mohammad Saber Fallah Nezhad Batul Rasti Bayesian Estimation of Shift Point in Shape Parameter of Inverse Gaussian Distribution Under Different Loss Functions Journal of Optimization in Industrial Engineering Bayes estimators shift point inverse Gaussian distribution loss function |
| title | Bayesian Estimation of Shift Point in Shape Parameter of Inverse Gaussian Distribution Under Different Loss Functions |
| title_full | Bayesian Estimation of Shift Point in Shape Parameter of Inverse Gaussian Distribution Under Different Loss Functions |
| title_fullStr | Bayesian Estimation of Shift Point in Shape Parameter of Inverse Gaussian Distribution Under Different Loss Functions |
| title_full_unstemmed | Bayesian Estimation of Shift Point in Shape Parameter of Inverse Gaussian Distribution Under Different Loss Functions |
| title_short | Bayesian Estimation of Shift Point in Shape Parameter of Inverse Gaussian Distribution Under Different Loss Functions |
| title_sort | bayesian estimation of shift point in shape parameter of inverse gaussian distribution under different loss functions |
| topic | Bayes estimators shift point inverse Gaussian distribution loss function |
| url | http://www.qjie.ir/article_216_0e38aaddfc4c867549097412e3c72196.pdf |
| work_keys_str_mv | AT mohammadsaberfallahnezhad bayesianestimationofshiftpointinshapeparameterofinversegaussiandistributionunderdifferentlossfunctions AT batulrasti bayesianestimationofshiftpointinshapeparameterofinversegaussiandistributionunderdifferentlossfunctions |