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The 'discrete case' given above is the special case arising when X takes on only countably many values and μ is a probability measure. In fact, the discrete case (although without the restriction to probability measures) is the first step in proving the general measure-theoretic formulation, as the general version follows therefrom by an ...
Given a measurable set S, a base probability distribution H and a positive real number, the Dirichlet process (,) is a stochastic process whose sample path (or realization, i.e. an infinite sequence of random variates drawn from the process) is a probability distribution over S, such that the following holds.
A dyadic distribution is a probability distribution whose probability mass function is = where is some whole number. It is possible to find a binary code defined on this distribution, which has an average code length that is equal to the entropy. [1]
Another way to express this is that the domain of the Dirichlet distribution is itself a set of probability distributions, specifically the set of K-dimensional discrete distributions. The technical term for the set of points in the support of a K -dimensional Dirichlet distribution is the open standard ( K − 1)-simplex , [ 3 ] which is a ...
A diagram of an alias table that represents the probability distribution〈0.25, 0.3, 0.1, 0.2, 0.15〉 In computing, the alias method is a family of efficient algorithms for sampling from a discrete probability distribution, published in 1974 by Alastair J. Walker.
The problem of estimating the maximum of a discrete uniform distribution on the integer interval [,] from a sample of k observations is commonly known as the German tank problem, following the practical application of this maximum estimation problem, during World War II, by Allied forces seeking to estimate German tank production.
These are also the three discrete distributions among the six members of the natural exponential family with quadratic variance functions (NEF–QVF). More general distributions can be defined by fixing some initial values of p j and applying the recursion to define subsequent values. This can be of use in fitting distributions to empirical data.
In probability theory and statistics, the Hermite distribution, named after Charles Hermite, is a discrete probability distribution used to model count data with more than one parameter. This distribution is flexible in terms of its ability to allow a moderate over-dispersion in the data.
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