scipy.special.ncfdtridfd

scipy.special.ncfdtridfd(dfn, p, nc, f, out=None) = <ufunc 'ncfdtridfd'>

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

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

Parameters

dfnarray_like

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

parray_like

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

ncarray_like

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

farray_like

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

outndarray, optional

Optional output array for the function results

Returns

dfdscalar or ndarray

Degrees of freedom of the denominator sum of squares.

See also

ncfdtr

CDF of the non-central F distribution.

ncfdtri

Quantile function; inverse of ncfdtr with respect to f.

ncfdtridfn

Inverse of ncfdtr with respect to dfn.

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, ncfdtridfd

Compute the CDF for several values of dfd:

>>> dfd = [1, 2, 3]
>>> p = ncfdtr(2, dfd, 0.25, 15)
>>> p
array([ 0.8097138 ,  0.93020416,  0.96787852])

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

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