scholarly journals Mixture Densities, Maximum Likelihood and the EM Algorithm

SIAM Review ◽  
1984 ◽  
Vol 26 (2) ◽  
pp. 195-239 ◽  
Author(s):  
Richard A. Redner ◽  
Homer F. Walker
Keyword(s):  
Maximum Likelihood ◽  
Em Algorithm ◽  
Mixture Densities ◽  
The Em Algorithm

Maximum-likelihood estimation in linkage heterogeneity models including additional information via the EM algorithm

1995 ◽  
Vol 12 (5) ◽  
pp. 515-527 ◽  
Author(s):  
Jeanine J. Houwing-Duistermaat ◽  
Lodewijk A. Sandkuijl ◽  
Arthur A. B. Bergen ◽  
Hans C. van Houwelingen
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Em Algorithm ◽  
Likelihood Estimation ◽  
Additional Information ◽  
The Em Algorithm

scholarly journals A New Generalized t Distribution Based on a Distribution Construction Method

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2413
Author(s):  
Ruijie Guan ◽  
Xu Zhao ◽  
Weihu Cheng ◽  
Yaohua Rong
Keyword(s):  
Maximum Likelihood ◽  
Em Algorithm ◽  
Iterative Algorithm ◽  
Likelihood Estimation ◽  
Estimation Methods ◽  
Modified Method ◽  
The Em Algorithm ◽  
Likelihood Approach ◽  
T Distribution ◽  
Better Than

In this paper, a new generalized t (new Gt) distribution based on a distribution construction approach is proposed and proved to be suitable for fitting both the data with high kurtosis and heavy tail. The main innovation of this article consists of four parts. First of all, the main characteristics and properties of this new distribution are outined. Secondly, we derive the explicit expression for the moments of order statistics as well as its corresponding variance–covariance matrix. Thirdly, we focus on the parameter estimation of this new Gt distribution and introduce several estimation methods, such as a modified method of moments (MMOM), a maximum likelihood estimation (MLE) using the EM algorithm, a novel iterative algorithm to acquire MLE, and improved probability weighted moments (IPWM). Through simulation studies, it can be concluded that the IPWM estimation performs better than the MLE using the EM algorithm and the MMOM in general. The newly-proposed iterative algorithm has better performance than the EM algorithm when the sample kurtosis is greater than 2.7. For four parameters of the new Gt distribution, a profile maximum likelihood approach using the EM algorithm is developed to deal with the estimation problem and obtain acceptable.

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