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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
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 Bates distribution is the distribution of the mean of n independent random variables, each of which having the uniform distribution on [0,1]. The logit-normal distribution on (0,1). The Dirac delta function , although not strictly a probability distribution, is a limiting form of many continuous probability functions.
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.
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.
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 Gaussian process is a stochastic process (a collection of random variables indexed by time or space), such that every finite collection of those random variables has a multivariate normal distribution. The distribution of a Gaussian process is the joint distribution of all those (infinitely many) random ...