scipy.special.ncfdtri#

scipy.special.ncfdtri(dfn, dfd, nc, p, out=None) = <ufunc 'ncfdtri'>#

Inverse with respect to f of the CDF of the non-central F distribution.

See ncfdtr for more details.

Parameters:

dfnarray_like: Degrees of freedom of the numerator sum of squares. Range (0, inf).
dfdarray_like: Degrees of freedom of the denominator sum of squares. Range (0, inf).
ncarray_like: Noncentrality parameter. Range [0, inf).
parray_like: Value of the cumulative distribution function. Must be in the range [0, 1].
outndarray, optional: Optional output array for the function results

Returns:

fscalar or ndarray: Quantiles, i.e., the upper limit of integration.

See also

ncfdtr: CDF of the non-central F distribution.
ncfdtridfd: Inverse of ncfdtr with respect to dfd.
ncfdtridfn: Inverse of ncfdtr with respect to dfn.
ncfdtrinc: Inverse of ncfdtr with respect to nc.
scipy.stats.ncf: Non-central F distribution.

Notes

This function calculates the Quantile of the non-central f distribution using the Boost Math C++ library [1].

Note that argument order of ncfdtri is different from that of the similar ppf method of scipy.stats.ncf. p is the last parameter of ncfdtri but the first parameter of scipy.stats.ncf.ppf.

References

[1]

The Boost Developers. “Boost C++ Libraries”. https://www.boost.org/.

Examples

>>> from scipy.special import ncfdtr, ncfdtri

Compute the CDF for several values of f:

>>> f = [0.5, 1, 1.5]
>>> p = ncfdtr(2, 3, 1.5, f)
>>> p
array([ 0.20782291,  0.36107392,  0.47345752])

Compute the inverse. We recover the values of f, as expected:

>>> ncfdtri(2, 3, 1.5, p)
array([ 0.5,  1. ,  1.5])