The Dirichlet distribution is a multivariate generalization of the beta distribution, commonly used in Bayesian statistics as a conjugate prior for the multinomial distribution. It is parameterized by a vector of positive values, α, which influences the shape of the distribution. The sum of the parameters, α₀ = ∑αᵢ, controls the concentration of the distribution. When all αᵢ are less than 1, the distribution exhibits spikes at the corners of the simplex, while values greater than 1 push the distribution towards the center, favoring equal probabilities among the outcomes ¹².

This distribution is particularly useful in modeling uncertainty in random vectors of probabilities, making it applicable in various fields such as Bayesian analysis, text mining, and statistical genetics. In practical applications, such as in the context of dice manufacturing, the Dirichlet distribution can help characterize the variability in outcomes and can be adjusted to produce fair or loaded dice by manipulating the parameters ¹³.

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