`scipy.stats._continuous_distns:ncf_gen`

source: /scipy/stats/_continuous_distns.py :7878

Signature

   class     ncf_gen (    momtype    =  1   ,    a    =  None   ,    b    =  None   ,    xtol    =  1e-14   ,    badvalue    =  None   ,    name    =  None   ,    longname    =  None   ,    shapes    =  None   ,    seed    =  None     )

Members

Summary

A non-central F distribution continuous random variable.

Extended Summary

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Notes

The probability density function for ncf is:

f (x, n_{1}, n_{2}, λ) = exp (\frac{λ}{2} + λ n_{1} \frac{x}{2 ( n _{1} x + n _{2} )}) n_{1}^{n_{1} /2} n_{2}^{n_{2} /2} x^{n_{1} /2 - 1} (n_{2} + n_{1} x)^{- (n_{1} + n_{2}) /2} γ (n_{1} /2) γ (1 + n_{2} /2) \frac{L _{n_{2} /2}^{\frac{n _{1}}{2} - 1} ( - λ n _{1} \frac{x}{2 ( n _{1} x + n _{2} )} )}{B ( n _{1} /2 , n _{2} /2 ) γ ( \frac{n _{1} + n _{2}}{2} )}

for $n_{1}, n_{2} > 0$ , $λ \geq 0$ . Here $n_{1}$ is the degrees of freedom in the numerator, $n_{2}$ the degrees of freedom in the denominator, $λ$ the non-centrality parameter, $γ$ is the logarithm of the Gamma function, $L_{n}^{k}$ is a generalized Laguerre polynomial and $B$ is the beta function.

ncf takes dfn, dfd and nc as shape parameters. If nc=0, the distribution becomes equivalent to the Fisher distribution.

This distribution uses routines from the Boost Math C++ library for the computation of the pdf, cdf, ppf, stats, sf and isf methods. ^[1]

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Aliases

scipy.stats._continuous_distns.ncf_gen