Товч агуулга:This thesis provides a comprehensive overview of finite mixture models, focusing on their theoretical foundations, diverse applications across various scientific fields, and the implementation of computer-intensive methods for their analysis. Finite mixture models are statistical tools used to represent populations composed of distinct subpopulations, making them valuable in addressing heterogeneity within data. The work delves into methodologies such as the Expectation-Maximization (EM) algorithm and explores applications in areas like clustering, classification, and pattern recognition.