![[LogDirichletDensity-alpha_0.3_to_alpha_2.0.gif|225]] # Dirichlet Distributions The Dirichlet distribution is a generalization of The Beta Function Dirichlet distributions are a popular prior distribution for categorical variables with $K$ categories. [Interactable Dirichlet Distribution Visualizer](https://observablehq.com/@herbps10/dirichlet-distribution) ## Probability Distribution Function $\frac{1}{B(\alpha)} \prod^{K}_{i=1}x_i^{\alpha_i-1}$ The *“means”* of a Dirichlet distribution refers to the mean of each random variable’s marginal density function. These can be used to plot a probability density function of the full multivariate distribution.