# Questions tagged [dirichlet-distribution]

The Dirichlet distribution refers to a family of multivariate distributions, which are the generalization of the univariate beta distribution.

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### How to generate data from a generalized Dirichlet distribution?

I need to generate data from a generalized Dirichlet distribution in Python to test my model, but I have no idea how can I proceed with that, can anyone guide me?
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### Concentration Bounds for categorial distribution with good Dirichlet prior

I would like to know if there are any standard methods for analyzing the concentration bounds (for example Hoeffding's bound) for a multinomial distribution modelled with a Dirichlet prior, with the ...
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### How to visualize Dirichlet distribution (with more than 3 targets)?

I want to plot a Dirichlet distribution $\operatorname{Dir}(\alpha), \alpha=[\alpha_1, \alpha_2, \ldots,\alpha_n]$. However, when I google it, almost all of the results consider 3 targets ($n=3$), and ...
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### Stationary distribution of a Markov chain with a random transition matrix

Consider a Markov chain $\{X_t\}$ on a finite state $\mathcal{S} = \{1,\dots, S\}$ space whose transition matrix $P$ is populated by elements of the form $$p_{ij} = P(X_{t+1} = j | X_t = i)$$ and we ...
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### Log-likelihood of a finite mixture distribution (PDF overflowing)

I'm trying to use a finite mixture of Dirichlet distributions in a project, but am encountering problems with the PDF becoming so large for input values close to 0 that it overflows to infinity (as ...
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### Upgrading weight parameters to random variable in Gaussian mixtures

In a Gaussian mixture model we model a density like: $p(\mathbf{x}|\pi,\mu,\sigma)=\sum \pi_i N(\mathbf{x}|\mu_i,\sigma_i)$  where $\pi,\mu$ and $\sigma$ are parameters. I would like to know if the ...
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