Concentration parameter: Difference between revisions

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In [[probability theory]] and [[statistics]], a '''concentration parameter''' is a special kind of [[numerical parameter]] of a [[parametric family]] of [[probability distribution]]s. Concentration parameters occur in two kinds of distribution: In the [[Von Mises–Fisher distribution]], and in conjunction with distributions whose ___domain is a probability distribution, such as the [[symmetric Dirichlet distribution]] and the [[Dirichlet process]]. The rest of this article focuses on the latter usage.

The larger the value of the concentration parameter, the more evenly distributed is the resulting distribution (the more it tends towards the [[Uniform distribution (continuous)|uniform distribution]]). The smaller the value of the concentration parameter, the more sparsely distributed is the resulting distribution, with most parametersvalues or ranges of values having a probability near zero (in other words, the more it tends towards a distribution concentrated on a single point, the [[degenerate distribution]] defined by the [[Dirac delta function]]).

In the case of multivariate Dirichlet distributions, there is some confusion over how to define the concentration parameter. In the topic modelling literature, it is often defined as the sum of the individual Dirichlet parameters,<ref>{{Cite conference