The chi-squared distribution χ k 2 {\displaystyle \chi _{k}^{2}} is a special case of the gamma distribution and the univariate Wishart distribution. Specifically...

variable and the origin. The chi distribution describes the positive square roots of a variable obeying a chi-squared distribution. If Z 1 , … , Z k {\displaystyle...

the noncentral chi-squared distribution (or noncentral chi-square distribution, noncentral χ 2 {\displaystyle \chi ^{2}} distribution) is a noncentral...

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

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

of scaled inverse chi-squared distributions is linked to the inverse-chi-squared distribution and to the chi-squared distribution: If X ∼ ψ inv- χ 2...

A chi-squared test (also chi-square or χ2 test) is a statistical hypothesis test used in the analysis of contingency tables when the sample sizes are...

Pearson's chi-squared test or Pearson's χ 2 {\displaystyle \chi ^{2}} test is a statistical test applied to sets of categorical data to evaluate how likely...

expected value of the squared deviation from the mean of a random variable. The standard deviation (SD) is obtained as the square root of the variance...

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...

The term chi-square, chi-squared, or χ 2 {\displaystyle \chi ^{2}} has various uses in statistics: chi-square distribution, a continuous probability distribution...

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

since the chi-squared distribution is the sum of squares of independent standard normal random variables, the random variable of the F-distribution may also...

2 {\displaystyle \chi ^{2}} has a chi-squared distribution with 1 degree of freedom. If the χ 2 {\displaystyle \chi ^{2}} result is significant, this...

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

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

the above chi-squared distribution with one degree of freedom, and the total energy will be distributed according to a chi-squared distribution with five...

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

F-distribution. It describes the distribution of the quotient (X/n1)/(Y/n2), where the numerator X has a noncentral chi-squared distribution with n1 degrees of freedom...

chi-squared distribution. Other related distributions may be seen there. If X {\displaystyle X} is chi distributed: X ∼ χ k {\displaystyle X\sim \chi...

correction modifies the standard chi-squared test to account for the fact that a continuous distribution (chi-squared) is used to approximate discrete...

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...

various uses, including the chi-squared distribution, the chi-squared test, and chi-squared target model In algebraic topology, Chi is used to represent the...

gamma distribution with shape parameter α = v/2 and rate parameter β = 1/2 is a chi-squared distribution with ν degrees of freedom. A chi-squared distribution...

{\textstyle |X-\mu |/\sigma \sim \chi _{1}} . The square of X / σ {\textstyle X/\sigma } has the noncentral chi-squared distribution with one degree of freedom:...

{Rice} (\nu ,1)} then R 2 {\displaystyle R^{2}} has a noncentral chi-squared distribution with two degrees of freedom and noncentrality parameter ν 2 {\displaystyle...

has a chi-squared distribution (χ2-distribution) with ν {\displaystyle \nu } degrees of freedom; Z and V are independent; A different distribution is defined...

determination (the R-squared measure of goodness of fit); Lack-of-fit sum of squares; Mallows's Cp criterion Prediction error Reduced chi-square The following...

\infty } , the distribution of the test statistic − 2 log ⁡ ( Λ ) {\displaystyle -2\log(\Lambda )} asymptotically approaches the chi-squared ( χ 2 {\displaystyle...