Dirichleteloszlású

Dirichleteloszlású is a Hungarian term that translates to "Dirichlet distributed" in English. It refers to a probability distribution that is a generalization of the beta distribution. The Dirichlet distribution is a continuous multivariate probability distribution that is parameterized by a vector of positive real numbers. It is commonly used in statistics and machine learning as a prior distribution for categorical distributions or multinomial distributions.

The Dirichlet distribution is defined over the standard simplex, which is the set of all vectors of length K whose components are non-negative and sum to 1. For a vector of parameters alpha = (alpha_1, alpha_2, ..., alpha_K), where alpha_i > 0 for all i, the probability density function of the Dirichlet distribution is given by:

f(x_1, x_2, ..., x_K; alpha_1, alpha_2, ..., alpha_K) = (1 / B(alpha)) * product(x_i^(alpha_i - 1)) for i = 1 to K

where B(alpha) is the multivariate beta function, which is a normalization constant.

The Dirichlet distribution is widely used in Bayesian inference, particularly in topic modeling (e.g., Latent Dirichlet Allocation - LDA) and natural language processing. It is also used in areas such as econometrics and bioinformatics. The parameters alpha influence the shape of the distribution. Higher values of alpha tend to result in distributions where the probabilities are more spread out, while lower values lead to more concentrated probabilities.