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name =Noncentral Beta| ...[continuous probability distribution]] that is a [[noncentral distribution|noncentral generalization]] of the (central) [[beta distribution]]. ...

...uced by Andrew&nbsp;F.&nbsp;Siegel in 1979.<ref>Siegel, A. F. (1979), "The noncentral chi-squared distribution with zero degrees of freedom and testing for unifo The noncentral chi-squared distribution with zero degrees of freedom and with noncentralit ...

...| title=Estimator and tests for common coefficients of variation in normal distributions | access-date=2013-09-23 |last1=Forkman |first1=Johannes |journal=Communica ...imately chi-square distributed, but exactly [[noncentral beta distribution|noncentral beta distributed]] ...

...mponents<br /><math>\boldsymbol{k}</math>, vector of degrees of freedom of noncentral chi-square components<br /><math>\boldsymbol{\lambda}</math>, vector of non ...is also a linear sum of independent [[noncentral chi-squared distribution|noncentral chi-square variables]] and a [[normal distribution|normal variable]]. There ...

== Probability distributions == ...tor and denominator are still independent. But the numerator then has a [[noncentral chi-squared distribution]], and consequently the quotient as a whole has a ...

...l_chi distribution|noncentral chi]], [[Noncentral chi-squared distribution|noncentral chi-squared]], and [[Rice distribution]]s. In engineering, this function ap ...ame="Temme1993">N.M. Temme (1993). Asymptotic and numerical aspects of the noncentral chi-square distribution. ''Computers Math. Applic.'', 25(5), 55-63.</ref> ...

...blem of testing for the equality of means from two [[multivariate normal]] distributions when the covariance matrices are unknown and possibly not equal. Since this ...andom samples from two [[multivariate normal|<math>p</math>-variate normal distributions]] with unknown mean vectors <math>\mu_i</math> and unknown [[covariance mat ...

...uct (mathematics)|product]] of [[random variable]]s having two other known distributions. Given two [[statistically independent]] random variables ''X'' and ''Y'', ...istribution]], sum distribution (see [[List of convolutions of probability distributions]]) and difference distribution. More generally, one may talk of combination ...