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	Wishart distribution - Wikipedia, the free encyclopedia
		In statistics, the Wishart distribution, named in honor of John Wishart, is any of a family of probability distributions for nonnegative-definite matrix-valued random variables ("random matrices").
		Noted statistician George Seber points out that the Wishart distribution is not called the "multivariate chi-square distribution" because the marginal distribution of the off-diagonal elements is not chi-square.
		The Wishart distribution is the probability distribution of the maximum-likelihood estimator (MLE) of the covariance matrix of a multivariate normal distribution.
	en.wikipedia.org /wiki/Wishart_distribution (494 words)

	Encyclopedia :: encyclopedia : Probability distribution (Site not responding. Last check: 2007-10-13)
		A probability distribution is a special case of the more general notion of a probability measure, which is a function that assigns probabilities satisfying the Kolmogorov axioms to the measurable sets of a measurable space.
		The rectangular distribution is a uniform distribution on [-1/2,1/2].
		The triangular distribution on [a, b], a special case of which is the distribution of the sum of two uniformly distributed random variables (the convolution of two uniform distributions).
	www.hallencyclopedia.com /Probability_distribution (1331 words)

	Probability distribution (Site not responding. Last check: 2007-10-13)
		A distribution is called discrete if its cumulative distribution function consists of a sequence of finite jumps,which means that it belongs to a discrete randomvariable X: a variable which can only attain values from a certain finite or countable set.
		The Weibull distribution, of which the exponentialdistribution is a special case, is used to model the lifetime of technical devices.
		The F-distribution, which is the distribution of the ratio of twonormally distributed random variables, used in the analysis ofvariance.
	www.therfcc.org /probability-distribution-29383.html (918 words)

	Estimation of covariance matrices - Wikipedia, the free encyclopedia
		In multivariate statistics, the importance of the Wishart distribution stems in part from the fact that it is the probability distribution of the maximum likelihood estimator of the covariance matrix of a multivariate normal distribution.
		Although no one is surprised that the estimator of the population covariance matrix is simply the sample covariance matrix, the mathematical derivation is perhaps not widely known and is surprisingly subtle and elegant.
		See the section on estimation in the article on the normal distribution for details; the process here is similar.
	en.wikipedia.org /wiki/Estimation_of_covariance_matrices (908 words)

	MultinormalDistribution
		The Wishart distribution is most typically used when describing the covariance matrix of multinormal samples.
		distribution is elliptically contoured like the multinormal distribution, and characterizes the ratio of a multinormal vector to the standard deviation common to each variate.
		This distribution is commonly used to describe the sample Mahalanobis distance between two populations.
	documents.wolfram.com /v5/Add-onsLinks/StandardPackages/Statistics/MultinormalDistribution.html (542 words)

	Wishart (print-only)
		Wishart was appointed to the Readership in the Faculty of Agriculture.
		The problem that Wishart's position caused at Cambridge was that he was too high powered a statistician for those in Agriculture but the mathematicians were also unhappy to send their students to the Faculty of Agriculture for statistics courses, and they would have much preferred to have statistics completely within Mathematics.
		Wishart died in a bathing accident in Acapulco, Mexico, which he was visiting as a representative of the United Nations Food and Agriculture Organisation to arrange setting up a research centre to apply statistical techniques in agricultural research.
	www-groups.dcs.st-and.ac.uk /history/Printonly/Wishart.html (957 words)

	Important Continuous Statistical Distributions in SEM
		The standard normal distribution, which constrains the mean to 0 and the variance to 1, is probably the most widely known statistical distribution.
		The mean of a chi-square distribution is equal to its degrees of freedom, and the variance is equal to twice the degrees of freedom.
		The Wishart distribution is the multivariate analog to the chi-square, and is related to the multivariate normal in the same way that the chi-square is related to the univariate normal.
	www2.gsu.edu /~mkteer/continuo.html (976 words)

	Probability distribution (Site not responding. Last check: 2007-10-13)
		A probability distribution is a special case the more general notion of a probability measure which is a function that assigns satisfying the Kolmogorov axioms to the measurable sets of a measurable space.
		The Beta distribution on [0 1] of which the distribution is a special case and which useful in estimating success probabilities.
		The Weibull distribution of which the exponential distribution is special case is used to model the of technical devices.
	www.freeglossary.com /Probability_Distributions (1249 words)

	Wishart distribution - Slider
		If ${\mathbf W} has a$ Wishart distribution with $m degrees of freedom and variance matrix {\mathbf V} ---write {\mathbf W}\sim{\mathbf W}_p(m,{\mathbf V}) ---and {\mathbf C} is a q\times p matrix of rank q, then$
		In this case, $\chi_m^2 is the chi-square$ distribution and $\sigma_z^2={\mathbf z'}{\mathbf V}{\mathbf z} (note that \sigma_z^2 is a constant; it is positive because {\mathbf V} is positive definite).$
		It involves the spectral theorem and the reason why it can be better to view a scalar as the trace of a 1×1 matrix than as a mere scalar.
	enc.slider.com /Enc/Wishart_distribution (445 words)

	Cumulant (Site not responding. Last check: 2007-10-13)
		All of the cumulants of the Poisson distribution are equal to the expected value.
		The simplest example is that the second cumulant of a probability distribution must always be nonnegative, and is zero only if all of the higher cumulants are zero.
		The Bell numbers are the moments of the Poisson distribution with expected value 1.
	www.serebella.com /encyclopedia/article-Cumulant.html (1130 words)

	Wishart distribution (Site not responding. Last check: 2007-10-13)
		In statistics, the Wishart distribution, named in honor of John Wishart, is any of a family of probability distribution s for nonnegative-definite matrix -valued random variable s ("random matrices"), defined as follows.
		is a p ×1 column-vector-valued random variable (a "random vector") that is normally distributed, whose expected value is the p ×1 column vector whose entries are all zero, and whose variance is the p × p nonnegative definite matrix V.
		The Wishart distribution arises frequently in likelihood-ratio test s in multivariate statistical analysis.
	www.serebella.com /encyclopedia/article-Wishart_distribution.html (994 words)

	[No title]
		Also, in the univariate (k=1) case, the Wishart distribution for W sub s in (Equation 3.4) becomes that of V tilde sub s of eta (now a scalar) times chi squared random variable with nu degrees of freedom.
		It is thus easy to see that the distribution for C sub s in the univariate case is that of a divided by open parenthesis a plus one close parenthesis all times V tilde sub s of eta times an F(nu, 2 times (a+1)) random variable.
		The random variance distribution was left unspecified by Kleffe and Rao, while Arora and Lahiri assumed a gamma distribution for the precisions (reciprocals of the variances).
	www.census.gov /hhes/www/saipe/asapaper/BellOtto95.txt (3222 words)

	Mathematica Documentation: MultinormalDistribution
		Functions such as Mean, which give properties of statistical distributions, take the symbolic representation of the distribution as an argument.
		distribution is a univariate distribution proportional to the F-ratio distribution.
		This gives the ellipse centered on the mean that encloses 50% of the ndist distribution.
	documents.wolfram.com /mathematica/Add-onsLinks/StandardPackages/Statistics/MultinormalDistribution.html (914 words)

	Wishart Random Numbers
		The Wishart distribution is a k-dimensional generalization of the chi-square distribution.
		The chi-square distribution is the sum of squared normal variates.
		The Wishart distribution is the sum of squared multivariate normal variates.
	www.itl.nist.gov /div898/software/dataplot/refman2/auxillar/wishrand.htm (379 words)

	UVa Statistics: Helene MASSAM
		But it is also apparent in the work on the decomposition of the li kelihood ratio statistic for testing the homogeneity of the covariances in several given samples from multivariate distributions.
		The Wishart distribution has many properties that are most efficiently analysed in the framework of Euclidean Jordan algebras and symmetric co nes.
		Wishart distributions are essential in the study of the traditional covariance selection model and the recently developped graphical models.
	www.stat.virginia.edu /massam.html (218 words)

	Dr. W. Y. Tan (Site not responding. Last check: 2007-10-13)
		On the distribution of number of mutants in cell populations with both forward and backward mutations.
		A stochastic model of HIV epidemic and the HIV infection distribution in a homosexual population.
		On the HIV Incubation Distribution of the HIV Epidemic.
	www.msci.memphis.edu /~waitan (3147 words)

	Hotelling's T-square distribution - Wikipedia, the free encyclopedia
		In statistics, Hotelling's T-square statistic, named for Harold Hotelling, is a generalization of Student's t statistic that is used in multivariate hypothesis testing.
		is a random variable with a multivariate normal distribution and
		has a Wishart distribution with m = n − 1 degrees of freedom and is independent of
	en.wikipedia.org /wiki/Hotelling's_T-square_distribution (302 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		The definition and some properties of Wishart and Inverted Wishart distributions will be discussed in the second part.
		The annual maximum precipitations are assumed to follow a multivariate log normal distribution and I use the Bayesian approach to estimate the mean vector and the covariance matrix.
		Wishart distribution is very useful in multivariate analysis because it is the generalization of Chi-square distribution, and because the inverted Wishart distribution is the conjugate prior distribution for the covariance matrix.
	www.stat.ubc.ca /people/grads/seventh.html (154 words)

	On the distribution of the largest eigenvalue in principal components analysis, Iain M. Johnstone
		Baik, J., Deift, P. and Johansson, K. On the distribution of the length of the longest increasing subsequence of random permutations.
		Forrester, P. Painlev´e transcendent evaluation of the scaled distribution of the smallest eigenvalue in the Laguerre orthogonal and symplectic ensembles.
		Wigner, E. On the distribution of the roots of certain symmetric matrices.
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.aos/1009210544 (734 words)

	Sankhya: The Indian Journal of Statistics (Site not responding. Last check: 2007-10-13)
		The noncentral Wishart distribution arises in various areas of multivariate analysis.
		The distribution is applicable in the study of the effect of changing values on the distribution of statistics computed from second order sample moments.
		It is therefore impractical to use the maximum likelihood method to estimate the parameters of the distribution.
	sankhya.isical.ac.in /search/52b2/52b2015.html (122 words)

	The Distribution and Moments of the Smallest Eigenvalue of a Random Matrix of Wishart Type -- from Mathematica ...
		Given a random rectangular m x n matrix with elements from a normal distribution, what is the distribution of the smallest singular value?
		To pose an equivalent question in the language of multivariate statistics, what is the distribution of the smallest eigenvalue of a matrix from the central Wishart distribution in the null case?
		With the recursion, one can obtain exact expressions for the density and the moments of the distribution in terms of functions usually no more complicated than polynomials, exponentials, and at worst ordinary hypergeometric function.
	library.wolfram.com /infocenter/Articles/2858 (185 words)

	Wishart distribution (Site not responding. Last check: 2007-10-13)
		In statistics, the Wishart distribution, named in honor ofJohn Wishart, is any of a family of probabilitydistributions for nonnegative-definite matrix -valued random variables ("random matrices"), defined as follows.
		is a p×1 column-vector-valued random variable (a "random vector") that is normally distributed, whose expected value is the p×1 column vector whose entries are all zero,and whose variance is the p×p nonnegative definite matrixV.
		Then the Wishart distribution is the probability distribution of the p×prandom matrix
	www.therfcc.org /wishart-distribution-206545.html (158 words)

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