Implementation of EM algorithm based on non-precise observations
The EM algorithm is a powerful tool and generic useful device in a variety of problems for maximum likelihood estimation with incomplete data which usually appears in practice. Here, the term ``incomplete" means a general state and in different situations it can mean different meanings, such as...
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| Format: | Article |
| Language: | English |
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Shahid Bahonar University of Kerman
2023-05-01
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| Series: | Journal of Mahani Mathematical Research |
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| Online Access: | https://jmmrc.uk.ac.ir/article_3623_45ee1cb26dac9f99b1965187f1093b39.pdf |
| _version_ | 1797799222208102400 |
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| author | Abbas Parchami |
| author_facet | Abbas Parchami |
| author_sort | Abbas Parchami |
| collection | DOAJ |
| description | The EM algorithm is a powerful tool and generic useful device in a variety of problems for maximum likelihood estimation with incomplete data which usually appears in practice. Here, the term ``incomplete" means a general state and in different situations it can mean different meanings, such as lost data, open source data, censored observations, etc. This paper introduces an application of the EM algorithm in which the meaning of ``incomplete" data is non-precise or fuzzy observations. The proposed approach in this paper for estimating an unknown parameter in the parametric statistical model by maximizing the likelihood function based on fuzzy observations. Meanwhile, this article presents a case study in the electronics industry, which is an extension of a well-known example used in introductions to the EM algorithm and focuses on the applicability of the algorithm in a fuzzy environment. This paper can be useful for graduate students to understand the subject in fuzzy environment and moreover to use the EM algorithm in more complex examples. |
| first_indexed | 2024-03-13T04:16:44Z |
| format | Article |
| id | doaj.art-77117ac1ddfa48a4afbb8768b2ceca4c |
| institution | Directory Open Access Journal |
| issn | 2251-7952 2645-4505 |
| language | English |
| last_indexed | 2024-03-13T04:16:44Z |
| publishDate | 2023-05-01 |
| publisher | Shahid Bahonar University of Kerman |
| record_format | Article |
| series | Journal of Mahani Mathematical Research |
| spelling | doaj.art-77117ac1ddfa48a4afbb8768b2ceca4c2023-06-21T03:19:53ZengShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-79522645-45052023-05-0112250351210.22103/jmmr.2023.20465.13573623Implementation of EM algorithm based on non-precise observationsAbbas Parchami0Department of Statistics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, IranThe EM algorithm is a powerful tool and generic useful device in a variety of problems for maximum likelihood estimation with incomplete data which usually appears in practice. Here, the term ``incomplete" means a general state and in different situations it can mean different meanings, such as lost data, open source data, censored observations, etc. This paper introduces an application of the EM algorithm in which the meaning of ``incomplete" data is non-precise or fuzzy observations. The proposed approach in this paper for estimating an unknown parameter in the parametric statistical model by maximizing the likelihood function based on fuzzy observations. Meanwhile, this article presents a case study in the electronics industry, which is an extension of a well-known example used in introductions to the EM algorithm and focuses on the applicability of the algorithm in a fuzzy environment. This paper can be useful for graduate students to understand the subject in fuzzy environment and moreover to use the EM algorithm in more complex examples.https://jmmrc.uk.ac.ir/article_3623_45ee1cb26dac9f99b1965187f1093b39.pdfem algorithmexponential distributionfuzzy statisticsfuzzy datamaximum likelihood estimation |
| spellingShingle | Abbas Parchami Implementation of EM algorithm based on non-precise observations Journal of Mahani Mathematical Research em algorithm exponential distribution fuzzy statistics fuzzy data maximum likelihood estimation |
| title | Implementation of EM algorithm based on non-precise observations |
| title_full | Implementation of EM algorithm based on non-precise observations |
| title_fullStr | Implementation of EM algorithm based on non-precise observations |
| title_full_unstemmed | Implementation of EM algorithm based on non-precise observations |
| title_short | Implementation of EM algorithm based on non-precise observations |
| title_sort | implementation of em algorithm based on non precise observations |
| topic | em algorithm exponential distribution fuzzy statistics fuzzy data maximum likelihood estimation |
| url | https://jmmrc.uk.ac.ir/article_3623_45ee1cb26dac9f99b1965187f1093b39.pdf |
| work_keys_str_mv | AT abbasparchami implementationofemalgorithmbasedonnonpreciseobservations |