2 {\displaystyle \chi ^{2}} -distribution with k {\displaystyle k} degrees of freedom is the distribution of a sum of the squares of k {\displaystyle...

statistics, the chi distribution is a continuous probability distribution over the non-negative real line. It is the distribution of the positive square root of...

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

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...

statistical procedures whose results are evaluated by reference to the chi-squared distribution. Its properties were first investigated by Karl Pearson in 1900...

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

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

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

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...

theorem shows that the unbiased sample variance S2 follows a scaled chi-squared distribution (see also: asymptotic properties and an elementary proof): ( n...

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

}}-{\boldsymbol {\mathbf {\mu } }})\sim \chi _{p}^{2},} where χ p 2 {\displaystyle \chi _{p}^{2}} is the chi-squared distribution with p degrees of freedom. If x...

and U 2 {\textstyle U_{2}} are independent random variables with chi-square distributions with respective degrees of freedom d 1 {\textstyle d_{1}} and d...

population distribution if a specified test statistic is too large, when that statistic would have approximately a chi-square distribution if the null...

statistical distribution of speeds is derived by equating particle energies with kinetic energy. Mathematically, the Maxwell–Boltzmann distribution is the chi distribution...

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...

identical distributions (see Kolmogorov–Smirnov test), or whether outcome frequencies follow a specified distribution (see Pearson's chi-square test). In...

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

distribution is a versatile two-parameter family of continuous probability distributions. The exponential distribution, Erlang distribution, and chi-squared...

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

noncentral chi distribution is a noncentral generalization of the chi distribution. It is also known as the generalized Rayleigh distribution. If X i {\displaystyle...

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

statistics, the reduced chi-square statistic is used extensively in goodness of fit testing. It is also known as mean squared weighted deviation (MSWD)...

number of individual radiators and considering the result using the chi-squared distribution: p ( σ ) = m Γ ( m ) σ a v ( m σ σ a v ) m − 1 e − m σ σ a v I...

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

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

{\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:...

model on a chi-square distribution with a single degree of freedom. If the predictor model has significantly smaller deviance (c.f. chi-square using the...

on the statistic whose sampling distribution is approximately a Chi-Square distribution with (k − 1) degrees of freedom, where k is the number of random...