Displaying similar documents to “On factorization of probability distributions over directed graphs”

Some properties and applications of probability distributions based on MacDonald function

Oldřich Kropáč (1982)

Aplikace matematiky

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In the paper the basic analytical properties of the MacDonald function (the modified Bessel function of the second kind) are summarized and the properties of some subclasses of distribution functions based on MacDonald function, especially of the types x n K n ( x ) , x ≥ 0 , x n K n ( x x ) , x ∈ 𝐑 and x n + 1 K n ( x ) , x ≥ 0 are discussed. The distribution functions mentioned are useful for analytical modelling of composed (mixed) distributions, especially for products of random variables having distributions of the exponential type. Extensive and...

Conditional problem for objective probability

Otakar Kříž (1998)

Kybernetika

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Marginal problem (see [Kel]) consists in finding a joint distribution whose marginals are equal to the given less-dimensional distributions. Let’s generalize the problem so that there are given not only less-dimensional distributions but also conditional probabilities. It is necessary to distinguish between objective (Kolmogorov) probability and subjective (de Finetti) approach ([Col,Sco]). In the latter, the coherence problem incorporates both probabilities and conditional probabilities...