Study on the Convergence Behavior of Expectation Maximization Algorithm for Laplace Mixture Model

Zakiah Ibrahim KALANTAN (
Faculty of Science, King Abdulaziz University, Saudi Arabia
MSc candidate Faten ALREWELY (
Faculty of Science, King Abdulaziz University, Saudi Arabia and Faculty of Science, Al Jouf University, Saudi Arabia
Kamarul Ariffin MANSOR (
Faculty of Computer Science and Mathematics, Universiti Teknologi MARA, Kedah, Malaysia


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.

Keywords: Laplace mixture model, Expectation-Maximization algorithm, Simulation case, R software.
JEL Classification: C13, C63

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Romanian Statistical Review 3/2019