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

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

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...

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

The noncentral beta distribution (Type I) is the distribution of the ratio X = χ m 2 ( λ ) χ m 2 ( λ ) + χ n 2 , {\displaystyle X={\frac {\chi _{m}^{2}(\lambda...

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

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...

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

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

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}}...

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...

{\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:...

(Fisher's z-distribution) The noncentral F-distribution simplifies to the F-distribution if λ = 0 {\displaystyle \lambda =0} . The doubly noncentral F-distribution...

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

The noncentral t distribution generalizes the t distribution to include a noncentrality parameter. Unlike the nonstandardized t distributions, the noncentral...

{\mu }})+k\ln(2\pi )\right]} , The circularly symmetric version of the noncentral complex case, where z {\displaystyle {\boldsymbol {z}}} is a vector of...

= 1 then this distribution is a chi-squared distribution with n degrees of freedom. The Wishart distribution arises as the distribution of the sample...

sum of squares above has a non-central chi-squared distribution with n degrees of freedom and "noncentrality parameter" μ 1 2 + ⋯ + μ n 2 . {\displaystyle...

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...

product distribution is a probability distribution constructed as the distribution of the product of random variables having two other known distributions. Given...

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...

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

noncentral F distribution. While with a given population standard deviation σ {\displaystyle \sigma } , the same test question applies noncentral chi-squared...

2(m-p+1)}.} Chi-squared distribution Dirichlet distribution F-distribution Gamma distribution Hotelling's T-squared distribution Student's t-distribution Wishart...

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

as a complementary cumulative distribution function for noncentral chi, noncentral chi-squared, and Rice distributions. In engineering, this function...

{\textrm {RSS}}/\sigma ^{2}} has a chi-squared distribution with k {\displaystyle k} degrees of freedom and noncentrality parameter λ {\displaystyle \lambda...

of any real-valued random variable completely defines its probability distribution. If a random variable admits a probability density function, then the...

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...