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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 ...
The Birnbaum–Saunders distribution, also known as the fatigue life distribution, is a probability distribution used extensively in reliability applications to model failure times. The chi distribution. The noncentral chi distribution; The chi-squared distribution, which is the sum of the squares of n independent Gaussian random variables.
A discrete probability distribution is applicable to the scenarios where the set of possible outcomes is discrete (e.g. a coin toss, a roll of a die) and the probabilities are encoded by a discrete list of the probabilities of the outcomes; in this case the discrete probability distribution is known as probability mass function.
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
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 ...
Arcsine distribution; Area chart; ... Crystal Ball function – a probability distribution; ... Student's t-test for Gaussian scale mixture distributions ...