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Density of a mixture of three normal distributions (μ = 5, 10, 15, σ = 2) with equal weights.Each component is shown as a weighted density (each integrating to 1/3) Given a finite set of probability density functions p 1 (x), ..., p n (x), or corresponding cumulative distribution functions P 1 (x),..., P n (x) and weights w 1, ..., w n such that w i ≥ 0 and ∑w i = 1, the mixture ...
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 ...
The Dirichlet distribution, a generalization of the beta distribution. The Ewens's sampling formula is a probability distribution on the set of all partitions of an integer n, arising in population genetics. The Balding–Nichols model; The multinomial distribution, a generalization of the binomial distribution.
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
Figure 1. A simple bimodal distribution, in this case a mixture of two normal distributions with the same variance but different means. The figure shows the probability density function (p.d.f.), which is an equally-weighted average of the bell-shaped p.d.f.s of the two normal distributions.
Any probability distribution can be decomposed as the mixture ... A discrete probability distribution is the ... rather than finding a closed formula for it. ...
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] (;) = /,, Rayleigh mixture distributions ...