EM algorithm for mixture of skew-normal distributions fitted to grouped data.

Area of Science:

• Statistics
• Computational Statistics

Background:

• Grouped data analysis is prevalent across various scientific disciplines.
• Traditional normal mixture models may not adequately capture data asymmetry.
• Accurate modeling of grouped data is crucial for reliable scientific insights.

Purpose of the Study:

• To apply the expectation-maximization (EM) algorithm for fitting skew-normal (SN) mixture models to grouped data.
• To evaluate the computational efficiency and accuracy of the EM algorithm for SN mixture models.
• To compare the performance of SN mixture models against traditional normal mixture models.

Main Methods:

• Utilized the expectation-maximization (EM) algorithm for parameter estimation.
• Employed the skew-normal (SN) mixture model to accommodate data asymmetry.
• Implemented the EM algorithm using the ForestFit package in the R environment.
• Conducted simulation studies and analyzed three real-world datasets.

Main Results:

• The EM algorithm demonstrated consistent convergence for SN mixture models.
• The EM algorithm provided rapid computations, even with a large number of components.
• The SN mixture model outperformed the normal mixture model in modeling grouped data.
• The ForestFit package facilitated efficient implementation.

Conclusions:

• The EM algorithm is a computationally efficient and accurate method for fitting SN mixture models to grouped data.
• SN mixture models offer superior performance compared to normal mixture models for asymmetric grouped data.
• The ForestFit R package provides a practical tool for implementing these advanced statistical methods.