The scaled inverse chi-squared distribution ψ inv- χ 2 ( ν ) {\displaystyle \psi \,{\mbox{inv-}}\chi ^{2}(\nu )} , where ψ {\displaystyle \psi } is the...

parametrize the inverse gamma distribution differently, as a scaled inverse chi-squared distribution. The inverse gamma distribution's probability density...

and statistics, the inverse-chi-squared distribution (or inverted-chi-square distribution) is a continuous probability distribution of a positive-valued...

Chi distribution Scaled inverse chi-squared distribution Gamma distribution Generalized chi-squared distribution Noncentral chi-squared distribution Pearson's...

Gamma distribution, and it is used in goodness-of-fit tests in statistics. The inverse-chi-squared distribution The noncentral chi-squared distribution The...

conjugate prior of the variance has an inverse gamma distribution or a scaled inverse chi-squared distribution. The two are equivalent except for having...

and statistics, the generalized chi-squared distribution (or generalized chi-square distribution) is the distribution of a quadratic function of a multinormal...

{\displaystyle \ \tau ^{2}~.} The scaled-inverse-chi-squared distribution is exactly the same distribution as the inverse gamma distribution, but with a different...

{\displaystyle X\,\sim \,\operatorname {Scale-inv-\chi ^{2}} (1,c)} (scaled-inverse-chi-squared distribution). If X ∼ Levy ⁡ ( μ , c ) {\displaystyle...

distribution, Erlang distribution, and chi-squared distribution are special cases of the gamma distribution. There are two equivalent parameterizations...

t-distribution was defined in terms of a scaled-inverse-chi-squared distribution placed on the variance. However, it is more common to use an inverse gamma...

\operatorname {K} (\alpha ,\beta )} (K-distribution) If also λ = 1/2 then X ∼ χ2 2; i.e., X has a chi-squared distribution with 2 degrees of freedom. Hence:...

negative. Other inverse distributions include inverse-chi-squared distribution inverse-gamma distribution inverse-Wishart distribution inverse matrix gamma...

chi-squared test) Student's t distribution, the distribution of the ratio of a standard normal variable and the square root of a scaled chi squared variable;...

Rayleigh distribution is a continuous probability distribution for nonnegative-valued random variables. Up to rescaling, it coincides with the chi distribution...

theory, the inverse Gaussian distribution (also known as the Wald distribution) is a two-parameter family of continuous probability distributions with support...

p ) {\displaystyle \chi _{k}^{2}(p)} is the quantile function for probability p {\displaystyle p} of the chi-squared distribution with k {\displaystyle...

Sazonov's theorem Saturated array Scale analysis (statistics) Scale parameter Scaled-inverse-chi-squared distribution Scaling pattern of occupancy Scatter...

In statistics, the inverse Wishart distribution, also called the inverted Wishart distribution, is a probability distribution defined on real-valued positive-definite...

In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures...

T-squared distribution (T2), proposed by Harold Hotelling, is a multivariate probability distribution that is tightly related to the F-distribution and...

{\displaystyle 2}{b}}\sum _{i=1}^{n}|X_{i}-\mu |\sim \chi ^{2}(2n)} (chi-squared distribution). If X , Y ∼ Laplace ( μ , b ) {\displaystyle X,Y\sim {\textrm...

be described as a scaled inverse chi-squared distribution, Scale-inv- χ 2 ( v 0 , s 0 2 ) . {\displaystyle {\text{Scale-inv-}}\chi ^{2}(v_{0},s_{0}^{2})...

calculation gives a scaled inverse chi-squared distribution with n − 1 degrees of freedom for the posterior probability distribution of σ2. The expected...

by an independent chi-distributed random variable, while the F-distribution originates from the ratio of two independent chi-squared distributed random...

Poisson distribution can be expressed using the relationship between the cumulative distribution functions of the Poisson and chi-squared distributions. The...

{\sigma {\sqrt {2}}}{\sqrt {\pi }}}} . Alternatively using a scaled precision (inverse of the variance) parametrization (to avoid issues if σ {\displaystyle...

approximation to the theoretical chi-squared distribution for the G-test is better than for the Pearson's chi-squared test. In cases where   O i > 2 ⋅...

Wishart distribution. Chi-squared distribution Complex Wishart distribution F-distribution Gamma distribution Hotelling's T-squared distribution Inverse-Wishart...

exponential gamma chi-squared beta Dirichlet Bernoulli categorical Poisson Wishart inverse Wishart geometric A number of common distributions are exponential...