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Implementation of EM algorithm based on non-precise observations | ||
| Journal of Mahani Mathematical Research | ||
| دوره 12، شماره 2 - شماره پیاپی 25، مرداد 2023، صفحه 503-512 اصل مقاله (775.39 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2023.20465.1357 | ||
| نویسنده | ||
| Abbas Parchami* | ||
| Department of Statistics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| EM algorithm؛ Exponential distribution؛ Fuzzy Statistics؛ Fuzzy data؛ Maximum likelihood estimation | ||
| مراجع | ||
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[1] G.M. Cordeiro, E.M.M. Ortega, and A.J. Lemonte, The exponential{Weibull lifetime distribution, Journal of Statistical Computation and Simulation 84 (2013) 2592{2606.
[2] A.P. Dempster, N.M. Laird, and D.B. Rubin, Maximum likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society 39 (1977) 1{38.
[3] T. Denoeux, Maximum likelihood estimation from fuzzy data using the EM algorithm, Fuzzy Sets and Systems 183 (2011) 72{91.
[4] B. Flury, and A. Zoppe, Exercises in EM, The American Statistician 54 (2000) 207{209.
[5] K. Knight, Mathematical Statistics, Chapman & Hall, New York, 2000.
[6] A. Parchami, EM.Fuzzy: EM algorithm for maximum likelihood estimation by non-precise information, R package version 1.0 (2018). URL: https://CRAN.R-project.org/package=EM.Fuzzy.
[7] R. Pourmousa, On truncated measures of income inequality from a fuzzy perspective, Iranian Journal of Fuzzy Systems 15 (2018) 123{137.
[8] L.A. Zadeh, Probability measures of fuzzy events, Journal of Mathematical Analysis and Applications 23 (1968) 421{427. | ||
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