Fitting A Mixture Distribution to Data: Tutorial
This is an incremental tutorial aimed at readers with basic calculus and linear algebra background, introducing model-based clustering as an application.
The paper provides a tutorial on fitting mixture distributions to data, covering both continuous and discrete cases with examples like Gaussian and Poisson mixtures, and includes numerical simulations for clarification.
This paper is a step-by-step tutorial for fitting a mixture distribution to data. It merely assumes the reader has the background of calculus and linear algebra. Other required background is briefly reviewed before explaining the main algorithm. In explaining the main algorithm, first, fitting a mixture of two distributions is detailed and examples of fitting two Gaussians and Poissons, respectively for continuous and discrete cases, are introduced. Thereafter, fitting several distributions in general case is explained and examples of several Gaussians (Gaussian Mixture Model) and Poissons are again provided. Model-based clustering, as one of the applications of mixture distributions, is also introduced. Numerical simulations are also provided for both Gaussian and Poisson examples for the sake of better clarification.