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Multivariate t-distribution, which is another widely used spherically symmetric multivariate distribution. Multivariate stable distribution extension of the multivariate normal distribution, when the index (exponent in the characteristic function) is between zero and two. Mahalanobis distance; Wishart distribution; Matrix normal distribution
In probability theory, Isserlis' theorem or Wick's probability theorem is a formula that allows one to compute higher-order moments of the multivariate normal distribution in terms of its covariance matrix. It is named after Leon Isserlis.
The probability density function for the random matrix X (n × p) that follows the matrix normal distribution , (,,) has the form: (,,) = ([() ()]) / | | / | | /where denotes trace and M is n × p, U is n × n and V is p × p, and the density is understood as the probability density function with respect to the standard Lebesgue measure in , i.e.: the measure corresponding to integration ...
The multivariate normal distribution is a special case of the elliptical distributions. As such, its iso-density loci in the k = 2 case are ellipses and in the case of arbitrary k are ellipsoids. Rectified Gaussian distribution a rectified version of normal distribution with all the negative elements reset to 0
In the event that the variables X and Y are jointly normally distributed random variables, then X + Y is still normally distributed (see Multivariate normal distribution) and the mean is the sum of the means. However, the variances are not additive due to the correlation. Indeed,
In terms of the circular variable = the circular moments of the wrapped normal distribution are the characteristic function of the normal distribution evaluated at integer arguments: z n = ∫ Γ e i n θ f W N ( θ ; μ , σ ) d θ = e i n μ − n 2 σ 2 / 2 . {\displaystyle \langle z^{n}\rangle =\int _{\Gamma }e^{in\theta }\,f_{WN}(\theta ...
In probability theory and statistics, a copula is a multivariate cumulative distribution function for which the marginal probability distribution of each variable is uniform on the interval [0, 1]. Copulas are used to describe/model the dependence (inter-correlation) between random variables . [ 1 ]
Nielsen [3] reported closed-form formula for calculating the Kullback-Leibler divergence and the Bhattacharyya distance between two truncated normal distributions with the support of the first distribution nested into the support of the second distribution.