family of scaled inverse chi-squared distributions is linked to the inverse-chi-squared distribution and to the chi-squared distribution: If X ∼ ψ inv-...

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

probability theory and statistics, the chi-squared distribution (also chi-square or χ 2 {\displaystyle \chi ^{2}} -distribution) with k {\displaystyle k} degrees...

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

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

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

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

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

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

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...

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

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

{\text{?}},{\text{?}},{\text{?}},{\text{?}})\,} normal-inverse chi-squared distribution G H ( ? , ? , ? , ? , ? ) {\displaystyle \mathrm {GH} ({\text{...

characteristics related to the chi-squared distribution. Let random variable Y be defined as Y = X2 where X has normal distribution with mean 0 and variance...

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

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

\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:...

^{2}}{\nu }},} where the chi-squared is a weighted sum of squared deviations: χ 2 = ∑ i ( O i − C i ) 2 σ i 2 {\displaystyle \chi ^{2}=\sum _{i}{\frac...

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

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

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

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

inequality Chernoff face Chernoff's distribution Chernoff's inequality Chi distribution Chi-squared distribution Chi-squared test Chinese restaurant process...

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;...

distribution (type III) Gamma distribution (type III) F-distribution (type VI) Inverse-chi-squared distribution (type V) Inverse-gamma distribution (type...

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

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

{\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...

it is apparent from the fact that for the chi-squared distribution the excess kurtosis is 12/k and the square of the skewness is 8/k, hence (excess kurtosis...

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