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In statistics, the inverse Wishart distribution, also called the inverted Wishart distribution, is a probability distribution defined on real-valued positive-definite matrices. In Bayesian statistics it is used as the conjugate prior for the covariance matrix of a multivariate normal distribution.
In probability theory and statistics, the normal-inverse-Wishart distribution (or Gaussian-inverse-Wishart distribution) is a multivariate four-parameter family of continuous probability distributions. It is the conjugate prior of a multivariate normal distribution with unknown mean and covariance matrix (the inverse of the precision matrix). [1]
The Wishart distribution is related to the inverse-Wishart distribution, denoted by , as follows: If X ~ W p (V, n) and if we do the change of variables C = X −1, then (,). This relationship may be derived by noting that the absolute value of the Jacobian determinant of this change of variables is | C | p +1 , see for example equation (15.15 ...
The complex inverse Wishart distribution is a matrix probability distribution defined on complex-valued positive-definite matrices and is the complex analog of the real inverse Wishart distribution. The complex Wishart distribution was extensively investigated by Goodman [ 1 ] while the derivation of the inverse is shown by Shaman [ 2 ] and others.
Inverse gamma distribution is a special case of type 5 Pearson distribution; A multivariate generalization of the inverse-gamma distribution is the inverse-Wishart distribution. For the distribution of a sum of independent inverted Gamma variables see Witkovsky (2001)
In statistics, the complex Wishart distribution is a complex version of the Wishart distribution. It is the distribution of n {\displaystyle n} times the sample Hermitian covariance matrix of n {\displaystyle n} zero-mean independent Gaussian random variables.
In statistics, the inverse matrix gamma distribution is a generalization of the inverse gamma distribution to positive-definite matrices. [1] It is a more general version of the inverse Wishart distribution, and is used similarly, e.g. as the conjugate prior of the covariance matrix of a multivariate normal distribution or matrix normal distribution.
Distribution of matrix inverse ... a useful property of the matrix variate beta distribution. Suppose , are independent Wishart matrices (,), (,). Assume ...