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- Mixture_distribution abstract "In probability and statistics, a mixture distribution is the probability distribution of a random variable whose values can be interpreted as being derived in the following way from an underlying set of other random variables: specifically, the realization of the random variable with a mixture distribution is randomly selected from among the realizations of the underlying random variables, with a certain probability of selection being associated with each. Here the underlying random variables may be random vectors (each having the same dimension) in which case the mixture distribution is a multivariate distribution.In cases where each of the underlying random variables is continuous, the outcome variable will also be continuous and its probability density function is sometimes referred to as a mixture density. The cumulative distribution function (and the probability density function if it exists) can be expressed as a convex combination (i.e. a weighted sum, with non-negative weights that sum to 1) of other distribution functions and density functions. The individual distributions that are combined to form the mixture distribution are called the mixture components, and the probabilities (or weights) associated with each component are called the mixture weights. The number of components in mixture distribution is often restricted to being finite, although in some cases the components may be countably infinite. More general cases (i.e. an uncountable set of component distributions), as well as the countable case, are treated under the title of compound distributions.A distinction needs to be made between a random variable whose distribution function or density is the sum of a set of components (i.e. a mixture distribution) and a random variable whose value is the sum of the values of two or more underlying random variables, in which case the distribution is given by the convolution operator. As an example, the sum of two jointly normally distributed random variables, each with different means, will still have a normal distribution. On the other hand, a mixture density created as a mixture of two normal distributions with different means will have two peaks provided that the two means are far enough apart, showing that this distribution is radically different from a normal distribution. Mixture distributions arise in many contexts in the literature and arise naturally where a statistical population contains two or more subpopulations. They are also sometimes used as a means of representing non-normal distributions. Data analysis concerning statistical models involving mixture distributions is discussed under the title of mixture models, while the present article concentrates on simple probabilistic and statistical properties of mixture distributions and how these relate to properties of the underlying distributions.".
- Mixture_distribution thumbnail Gaussian-mixture-example.svg?width=300.
- Mixture_distribution wikiPageID "708242".
- Mixture_distribution wikiPageRevisionID "596938958".
- Mixture_distribution hasPhotoCollection Mixture_distribution.
- Mixture_distribution subject Category:Probability_distributions.
- Mixture_distribution subject Category:Systems_of_probability_distributions.
- Mixture_distribution type Artifact100021939.
- Mixture_distribution type Instrumentality103575240.
- Mixture_distribution type Object100002684.
- Mixture_distribution type PhysicalEntity100001930.
- Mixture_distribution type System104377057.
- Mixture_distribution type SystemsOfProbabilityDistributions.
- Mixture_distribution type Whole100003553.
- Mixture_distribution comment "In probability and statistics, a mixture distribution is the probability distribution of a random variable whose values can be interpreted as being derived in the following way from an underlying set of other random variables: specifically, the realization of the random variable with a mixture distribution is randomly selected from among the realizations of the underlying random variables, with a certain probability of selection being associated with each.".
- Mixture_distribution label "Mixture distribution".
- Mixture_distribution sameAs m.034lf0.
- Mixture_distribution sameAs Q17157111.
- Mixture_distribution sameAs Q17157111.
- Mixture_distribution sameAs Mixture_distribution.
- Mixture_distribution wasDerivedFrom Mixture_distribution?oldid=596938958.
- Mixture_distribution depiction Gaussian-mixture-example.svg.
- Mixture_distribution isPrimaryTopicOf Mixture_distribution.
