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In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the ...
The chi-squared distribution, which is the sum of the squares of n independent Gaussian random variables. It is a special case of the Gamma distribution, and it is used in goodness-of-fit tests in statistics. The inverse-chi-squared distribution; The noncentral chi-squared distribution; The scaled inverse chi-squared distribution; The Dagum ...
In statistics, a sum of squares due to lack of fit, or more tersely a lack-of-fit sum of squares, is one of the components of a partition of the sum of squares of residuals in an analysis of variance, used in the numerator in an F-test of the null hypothesis that says that a proposed model fits well.
Up to a multiplicative factor, the squared Mahalanobis distance is a special case of the Bhattacharyya distance when the two classes are normally distributed with the same variances. When two classes have similar means but significantly different variances, the Mahalanobis distance would be close to zero, while the Bhattacharyya distance would ...
In information geometry, a divergence is a kind of statistical distance: a binary function which establishes the separation from one probability distribution to another on a statistical manifold. The simplest divergence is squared Euclidean distance (SED), and divergences can be viewed as generalizations of SED.
In the case where a parametrized family has a location parameter, a slightly different definition is often used as follows.If we denote the location parameter by , and the scale parameter by , then we require that (;,,) = (() /;,,) where (,,,) is the cmd for the parametrized family. [1]
To define the Hellinger distance in terms of elementary probability theory, we take λ to be the Lebesgue measure, so that dP / dλ and dQ / dλ are simply probability density functions. If we denote the densities as f and g, respectively, the squared Hellinger distance can be expressed as a standard calculus integral
In probability theory and statistics, the law of the unconscious statistician, or LOTUS, is a theorem which expresses the expected value of a function g(X) of a random variable X in terms of g and the probability distribution of X. The form of the law depends on the type of random variable X in question.