Study on the Convergence Behavior of Expectation Maximization Algorithm for Laplace Mixture Model
Laplace mixture model is widely used in lifetime applications. The estimation of model parameters is required to analyze the data. In this paper, the expectation maximization algorithm is used to obtain the estimates of parameters. The algorithm is a widely applicable approach to the iterative compu...
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2019-09-01
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doaj-c2d711ab6310402c953c7f5d8a93cf062020-11-25T03:01:06ZengRomanian National Institute of StatisticsRevista Română de Statistică1018-046X1844-76942019-09-016733545Study on the Convergence Behavior of Expectation Maximization Algorithm for Laplace Mixture ModelZakiah Ibrahim KALANTAN0Faten ALREWELY1Kamarul Ariffin MANSOR2Faculty of Science, King Abdulaziz University, Saudi ArabiaFaculty of Science, King Abdulaziz University, Saudi Arabia and Faculty of Science, Al Jouf University, Saudi ArabiaFaculty of Computer Science and Mathematics, Universiti Teknologi MARA, Kedah, MalaysiaLaplace mixture model is widely used in lifetime applications. The estimation of model parameters is required to analyze the data. In this paper, the expectation maximization algorithm is used to obtain the estimates of parameters. The algorithm is a widely applicable approach to the iterative computation of the maximum likelihood estimates. However, even though the algorithm is useful for more than two components, we discuss it for a two components Laplace mixture model for simplicity. The behavior of the algorithm is explained with mathematical proofs. We also study the parameter estimates with respect to various sample sizes. The implementation of the expectation maximization algorithm is made via functions written in R script. The performance of the algorithm is guaranteed the convergent to a local maximum of the data log-likelihood model as a function of the model parameters. In addition, the results shown that the estimated parameters are closed to the real parameter values when the sample size is large.http://www.revistadestatistica.ro/wp-content/uploads/2019/09/A4_RRS-3_20191.pdflaplace mixture modelexpectation-maximization algorithmsimulation caser software |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Zakiah Ibrahim KALANTAN Faten ALREWELY Kamarul Ariffin MANSOR |
spellingShingle |
Zakiah Ibrahim KALANTAN Faten ALREWELY Kamarul Ariffin MANSOR Study on the Convergence Behavior of Expectation Maximization Algorithm for Laplace Mixture Model Revista Română de Statistică laplace mixture model expectation-maximization algorithm simulation case r software |
author_facet |
Zakiah Ibrahim KALANTAN Faten ALREWELY Kamarul Ariffin MANSOR |
author_sort |
Zakiah Ibrahim KALANTAN |
title |
Study on the Convergence Behavior of Expectation Maximization Algorithm for Laplace Mixture Model |
title_short |
Study on the Convergence Behavior of Expectation Maximization Algorithm for Laplace Mixture Model |
title_full |
Study on the Convergence Behavior of Expectation Maximization Algorithm for Laplace Mixture Model |
title_fullStr |
Study on the Convergence Behavior of Expectation Maximization Algorithm for Laplace Mixture Model |
title_full_unstemmed |
Study on the Convergence Behavior of Expectation Maximization Algorithm for Laplace Mixture Model |
title_sort |
study on the convergence behavior of expectation maximization algorithm for laplace mixture model |
publisher |
Romanian National Institute of Statistics |
series |
Revista Română de Statistică |
issn |
1018-046X 1844-7694 |
publishDate |
2019-09-01 |
description |
Laplace mixture model is widely used in lifetime applications. The estimation of model parameters is required to analyze the data. In this paper, the expectation maximization algorithm is used to obtain the estimates of parameters. The algorithm is a widely applicable approach to the iterative computation of the maximum likelihood estimates. However, even though the algorithm is useful for more than two components, we discuss it for a two components Laplace mixture model for simplicity. The behavior of the algorithm is explained with mathematical proofs. We also study the parameter estimates with respect to various sample sizes. The implementation of the expectation maximization algorithm is made via functions written in R script. The performance of the algorithm is guaranteed the convergent to a local maximum of the data log-likelihood model as a function of the model parameters. In addition, the results shown that the estimated parameters are closed to the real parameter values when the sample size is large. |
topic |
laplace mixture model expectation-maximization algorithm simulation case r software |
url |
http://www.revistadestatistica.ro/wp-content/uploads/2019/09/A4_RRS-3_20191.pdf |
work_keys_str_mv |
AT zakiahibrahimkalantan studyontheconvergencebehaviorofexpectationmaximizationalgorithmforlaplacemixturemodel AT fatenalrewely studyontheconvergencebehaviorofexpectationmaximizationalgorithmforlaplacemixturemodel AT kamarulariffinmansor studyontheconvergencebehaviorofexpectationmaximizationalgorithmforlaplacemixturemodel |
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1724694952071397376 |