# Fitting A Mixture Distribution to Data: Tutorial

arXiv: https://arxiv.org/abs/1901.06708 · HTML: https://mlsanity.com/paper/1901.06708/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jan 2019.

## Built on by (most cited first, 6 of 6)

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- [Generative Adversarial Networks and Adversarial Autoencoders: Tutorial and Survey](https://mlsanity.com/paper/2111.13282/) (2021)
- [Wittgenstein's Family Resemblance Clustering Algorithm](https://mlsanity.com/paper/2601.01127/) (2026)
- [Discrete Tree Flows via Tree-Structured Permutations](https://mlsanity.com/paper/2207.01744/) (2022)
- [Classification with Trust: A Supervised Approach based on Sequential Ellipsoidal Partitioning](https://mlsanity.com/paper/2302.10487/) (2023)
- [Probabilistic Classification by Density Estimation Using Gaussian Mixture Model and Masked Autoregressive Flow](https://mlsanity.com/paper/2310.10843/) (2023)

## Abstract (arXiv)

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.