This distribution is sometimes called the central chi-squared distribution, a special case of the more general noncentral chi-squared distribution. The...

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

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...

the noncentral chi distribution is a noncentral generalization of the chi distribution. It is also known as the generalized Rayleigh distribution. If...

distribution. The generalized chi-squared variable may be described in multiple ways. One is to write it as a weighted sum of independent noncentral chi-square...

to the chi-squared distribution by describing the distribution of the positive square roots of a variable obeying a chi-squared distribution. If Z 1...

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

following distributions: Noncentral t-distribution Noncentral chi-squared distribution Noncentral chi-distribution Noncentral F-distribution Noncentral beta...

_{m}^{2}(\lambda )}{\chi _{m}^{2}(\lambda )+\chi _{n}^{2}}},} where χ m 2 ( λ ) {\displaystyle \chi _{m}^{2}(\lambda )} is a noncentral chi-squared random variable...

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

The noncentral t-distribution generalizes Student's t-distribution using a noncentrality parameter. Whereas the central probability distribution describes...

shared with the noncentral chi-squared distribution. Karl Pearson (Pearson 1895, pp. 357, 360, 373–376) also showed that the gamma distribution is a Pearson...

F-distribution with parameters d 1 {\displaystyle d_{1}} and d 2 {\displaystyle d_{2}} arises as the ratio of two appropriately scaled chi-squared variates:...

beta prime distribution If V 1 ∼ χ ′ k 1 2 ( λ ) {\displaystyle V_{1}\sim {\chi '}_{k_{1}}^{2}(\lambda )} , a noncentral chi-squared distribution, and V 2...

Equivalently, this distribution results from compounding a Gaussian distribution with a scaled-inverse-chi-squared distribution with parameters ν {\displaystyle...

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

n_{x}+n_{y}-1-p).} The non-null distribution of this statistic is the noncentral F-distribution (the ratio of a non-central Chi-squared random variable and an...

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

numerator then has a noncentral chi-squared distribution, and consequently the quotient as a whole has a non-central F-distribution. One uses this F-statistic...

When μ = 0, the distribution of Y is a half-normal distribution. The random variable (Y/σ)2 has a noncentral chi-squared distribution with 1 degree of...

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

category Noncentral beta distribution Noncentral chi distribution Noncentral chi-squared distribution Noncentral F-distribution Noncentral hypergeometric...

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

square root of the chi-squared statistic divided by the sample size. Similarly, Cramér's V is computed by taking the square root of the chi-squared statistic...

)^{2}/(2\sigma ^{2})}).} This is a noncentral chi-squared distribution with one degree of freedom. The probability distribution of the sum of two independent...

however, the statistics converge to a noncentral chi-squared distribution with possibly different noncentrality parameters. A more general score test...

independent, then the sum of squares above has a non-central chi-squared distribution with n degrees of freedom and "noncentrality parameter" μ 1 2 + ⋯ + μ...

based on the noncentral t-distribution. Two-sided normal tolerance intervals can be obtained based on the noncentral chi-squared distribution. "In the parameters-known...

\;\;{\text{ as }}\rho \rightarrow 1\\\end{aligned}}} which is a Chi-squared distribution with one degree of freedom. Multiple correlated samples. Nadarajaha...

elliptical distribution is any member of a broad family of probability distributions that generalize the multivariate normal distribution. Intuitively...