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In probability and statistics, a mixture distribution is the probability distribution of a random variable that is derived from a collection of other random variables as follows: first, a random variable is selected by chance from the collection according to given probabilities of selection, and then the value of the selected random variable is realized.
In probability and statistics, a compound probability distribution (also known as a mixture distribution or contagious distribution) is the probability distribution that results from assuming that a random variable is distributed according to some parametrized distribution, with (some of) the parameters of that distribution themselves being random variables.
In probability theory and statistics, a mixture is a probabilistic combination of two or more probability distributions. [1] The concept arises mostly in two contexts: A mixture defining a new probability distribution from some existing ones, as in a mixture distribution or a compound distribution. Here a major problem often is to derive the ...
A typical finite-dimensional mixture model is a hierarchical model consisting of the following components: . N random variables that are observed, each distributed according to a mixture of K components, with the components belonging to the same parametric family of distributions (e.g., all normal, all Zipfian, etc.) but with different parameters
This category is collections of probability distribution that have been brought together for a similar usage in Statistics to the Pearson system of distributions, or the Burr system. That is to have distributions that between them cover a range of behaviour that is not covered by any single one, such that a statistical analysis would select a ...
An important example of normal variance-mean mixtures is the generalised hyperbolic distribution in which the mixing distribution is the generalized inverse Gaussian distribution. The probability density function of a normal variance-mean mixture with mixing probability density g {\displaystyle g} is
In probability theory and statistics a Rayleigh mixture distribution is a weighted mixture of multiple probability distributions where the weightings are equal to the weightings of a Rayleigh distribution. [1] Since the probability density function for a (standard) Rayleigh distribution is given by [2]
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