# scipy.special.ncfdtridfn#

scipy.special.ncfdtridfn(p, dfd, nc, f, out=None) = <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.

outndarray, optional

Optional output array for the function results

Returns:
dfnscalar or ndarray

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.])
```