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Suppose G is a p × n matrix, each column of which is independently drawn from a p-variate normal distribution with zero mean: = (, …,) (,). Then the Wishart distribution is the probability distribution of the p × p random matrix [4]
For the special case of correlation matrices, we know that = and = /.This bounds the probability mass over the interval defined by = (). Since this distribution describes the spectrum of random matrices with mean 0, the eigenvalues of correlation matrices that fall inside of the aforementioned interval could be considered spurious or noise.
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.
English: A selection of Normal Distribution Probability Density Functions (PDFs). Both the mean, μ , and variance, σ² , are varied. The key is given on the graph.
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A substochastic matrix is a real square matrix whose row sums are all ; In the same vein, one may define a probability vector as a vector whose elements are nonnegative real numbers which sum to 1. Thus, each row of a right stochastic matrix (or column of a left stochastic matrix) is a probability vector.
In probability theory and statistics, the Rademacher distribution (which is named after Hans Rademacher) is a discrete probability distribution where a random variate X has a 50% chance of being +1 and a 50% chance of being −1.