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The uniform distribution or rectangular distribution on [a,b], where all points in a finite interval are equally likely, is a special case of the four-parameter Beta distribution. The Irwin–Hall distribution is the distribution of the sum of n independent random variables, each of which having the uniform distribution on [0,1].
Marshall–Olkin exponential distribution; Matrix gamma distribution; Matrix normal distribution; Matrix-exponential distribution; Maximum entropy probability distribution; Maxwell–Boltzmann distribution; McCullagh's parametrization of the Cauchy distributions; Metalog distribution; Mittag-Leffler distribution; Moffat distribution; Multimodal ...
If the covariance matrix is not full rank, then the multivariate normal distribution is degenerate and does not have a density. More precisely, it does not have a density with respect to k -dimensional Lebesgue measure (which is the usual measure assumed in calculus-level probability courses).
Throughout this article, boldfaced unsubscripted and are used to refer to random vectors, and Roman subscripted and are used to refer to scalar random variables.. If the entries in the column vector = (,, …,) are random variables, each with finite variance and expected value, then the covariance matrix is the matrix whose (,) entry is the covariance [1]: 177 ...
Marchenko–Pastur distribution; Matrix variate Dirichlet distribution; Modified half-normal distribution; Modified Kumaraswamy distribution; Multivariate Laplace distribution; Multivariate logistic distribution
Several important classes of matrices are subsets of each other. This article lists some important classes of matrices used in mathematics, science and engineering. A matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers called entries. Matrices have a long history of both study and application, leading to ...
In nuclear physics, random matrices were introduced by Eugene Wigner to model the nuclei of heavy atoms. [1] [2] Wigner postulated that the spacings between the lines in the spectrum of a heavy atom nucleus should resemble the spacings between the eigenvalues of a random matrix, and should depend only on the symmetry class of the underlying evolution. [4]
The Wishart distribution arises as the distribution of the sample covariance matrix for a sample from a multivariate normal distribution. It occurs frequently in likelihood-ratio tests in multivariate statistical analysis. It also arises in the spectral theory of random matrices [citation needed] and in multidimensional Bayesian analysis. [5]