# scipy.special.ncfdtridfn¶

scipy.special.ncfdtridfn(p, dfd, nc, f) = <ufunc 'ncfdtridfn'>

Calculate degrees of freedom (numerator) for the noncentral F-distribution.

This is the inverse with respect to dfn of ncfdtr. See ncfdtr for more details.

Parameters
parray_like

Value of the cumulative distribution function. Must be in the range [0, 1].

dfdarray_like

Degrees of freedom of the denominator sum of squares. Range (0, inf).

ncarray_like

Noncentrality parameter. Should be in range (0, 1e4).

ffloat

Quantiles, i.e., the upper limit of integration.

Returns
dfnfloat

Degrees of freedom of the numerator sum of squares.

ncfdtr

CDF of the non-central F distribution.

ncfdtri

Quantile function; inverse of ncfdtr with respect to f.

ncfdtridfd

Inverse of ncfdtr with respect to dfd.

ncfdtrinc

Inverse of ncfdtr with respect to nc.

Notes

The value of the cumulative noncentral F distribution is not necessarily monotone in either degrees of freedom. There thus may be two values that provide a given CDF value. This routine assumes monotonicity and will find an arbitrary one of the two values.

Examples

>>> from scipy.special import ncfdtr, ncfdtridfn

Compute the CDF for several values of dfn:

>>> dfn = [1, 2, 3]
>>> p = ncfdtr(dfn, 2, 0.25, 15)
>>> p
array([ 0.92562363,  0.93020416,  0.93188394])

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

>>> ncfdtridfn(p, 2, 0.25, 15)
array([ 1.,  2.,  3.])

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