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...family of continuous [[probability distribution]]s. It is the [[conjugate prior]] of a [[multivariate normal distribution]] with unknown [[mean]] and [[pre ===Marginal distributions=== ...

...tribution]] resulting from compounding a matrix normal with a matrix gamma prior over the precision matrix is a [[generalized matrix t-distribution]].<ref n A matrix gamma distributions is identical to a [[Wishart distribution]] with <math>\beta \boldsymbol\Sig ...

{{Short description|Multivariate parameter family of continuous probability distributions}} ...of the [[precision matrix]]).<ref name="murphy">Murphy, Kevin P. (2007). "Conjugate Bayesian analysis of the Gaussian distribution." [http://www.cs.ubc.ca/~mur ...

...]] resulting from compounding a matrix normal with an inverse matrix gamma prior over the covariance matrix is a [[generalized matrix t-distribution]].{{cit [[Category:Continuous distributions]] ...

==Prior vs. posterior predictive distribution== ...{x}|\theta)</math> and <math>\theta \sim G(\theta|\alpha)</math>, then the prior predictive distribution is the corresponding distribution <math>H(\tilde{x} ...

...ris |last2=Pericchi |first2=Luis Raúl |date=2018-12-01 |title=The Matrix-F Prior for Estimating and Testing Covariance Matrices |journal=Bayesian Analysis | ...ally derived by.<ref name="olkinrubin1964" /> When considering independent distributions, ...

...ltivariate continuous [[probability distribution]]s. It is the [[conjugate prior]] of a [[normal distribution]] with unknown [[mean]] and [[variance]]. ===Marginal distributions=== ...

The authors went on to use these distributions in the context of three different applications in medical science. [[Category:Multivariate continuous distributions]] ...

The inverted Dirichlet distribution is conjugate to the [[negative multinomial distribution]] if a generalized form of [[odd ...ce|isbn=978-3-642-24957-0}}</ref> [[mixture models]] of inverted Dirichlet distributions using the [[Newton–Raphson]] technique to estimate the parameters and the [ ...

===Marginal distributions=== ===Conditional distributions=== ...

==Eigenvalue distributions== ...paper by James.<ref>{{Cite journal|last=James|first=A. T.|date=1964|title=Distributions of Matrix Variates and Latent Roots Derived from Normal Samples.|journal=An ...

== Related distributions == *The [[gamma distribution]] is a natural [[conjugate prior]] to a Gompertz likelihood with known, scale parameter <math>b \,\!.</math> ...

...ssian zero-mean samples and <math> (.)^H </math> is an Hermitian (complex conjugate) transpose. If the covariance of '''''G''''' is <math> \mathbb{E}[GG^H] = ...r example, James<ref>{{Cite journal|last=James|first=A. T.|date=1964|title=Distributions of Matrix Variates and Latent Roots Derived from Normal Samples|journal=Ann ...

...distributions.jpg|thumb|Relationships among some of univariate probability distributions are illustrated with connected lines. dashed lines means approximate relati ...pages=2719–21 | title=ProbOnto: ontology and knowledge base of probability distributions | year=2016 | journal=Bioinformatics | last1 = Swat | first1 = MJ | last2 = ...

...he form of a quadrature rule whose weights are determined by the choice of prior. ...ribution on <math> \nu[f] </math>. Suppose we have a Gaussian process with prior mean function <math> m: \mathcal{X} \rightarrow \mathbb{R} </math> and [[co ...

...and <math>f_2</math> are the probability density functions of two Gompertz distributions, then their [[Kullback-Leibler divergence]] is given by ..., C. (2014), Characterizations and Kullback-Leibler Divergence of Gompertz Distributions, {{arXiv|1402.3193}}.</ref> ...

...me prior distribution for the total number of balls in the urn, and a beta prior distribution with parameters ''(x,y)'' for the initial proportion of these ==Distributions related to the Pólya urn== ...

...</ref> and the use of the volume element as a candidate for the [[Jeffreys prior]] probability density<ref>{{cite journal | last=Slater | first=Paul B. | t ...h>. The Wootters distance is the geodesic distance between the probability distributions <math>p, q </math> under the [[Chi-squared divergence|chi-squared]] metric< ...

| conjugate prior = [[Category:Probability distributions]] ...

...n was discovered by Stephen Lihn (Chinese: 藺鴻圖) in his 2017 study of daily distributions of the [[S&P 500]] and the [[VIX]].<ref name=":4" /> The stable distributio ...he stability parameter <math>\alpha</math> is most important. Stable count distributions have <math>0<\alpha<1</math>. The known analytical case of <math>\alpha=1/2 ...