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SciPy

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scipy.special.fdtri

scipy.special.fdtri(dfn, dfd, p) = <ufunc 'fdtri'>

The p-th quantile of the F-distribution.

This function is the inverse of the F-distribution CDF, fdtr, returning the x such that fdtr(dfn, dfd, x) = p.

Parameters:

dfn : array_like

First parameter (positive float).

dfd : array_like

Second parameter (positive float).

p : array_like

Cumulative probability, in [0, 1].

Returns:

x : ndarray

The quantile corresponding to p.

Notes

The computation is carried out using the relation to the inverse regularized beta function, I1x(a,b). Let z=I1p(dd/2,dn/2). Then,

x=dd(1z)dnz.

If p is such that x<0.5, the following relation is used instead for improved stability: let z=I11p(dn/2,dd/2). Then,

x=ddzdn(1z).

Wrapper for the Cephes [R359] routine fdtri.

References

[R359](1, 2) Cephes Mathematical Functions Library, http://www.netlib.org/cephes/index.html

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