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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 discrete probability distribution is the probability distribution ... and the science of statistics. ... Such quantities can be modeled using a mixture distribution ...
The Irwin–Hall distribution is the distribution of the sum of n independent random variables, each of which having the uniform distribution on [0,1]. The Bates distribution is the distribution of the mean of n independent random variables, each of which having the uniform distribution on [0,1]. The logit-normal distribution on (0,1).
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
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
It is called "mixed logit" because the choice probability is a mixture of logits, with as the mixing distribution. [2] It has been shown that a mixed logit model can approximate to any degree of accuracy any true random utility model of discrete choice, given appropriate specification of variables and the coefficient distribution.