# scipy.special.fdtr#

scipy.special.fdtr(dfn, dfd, x, out=None) = <ufunc 'fdtr'>#

F cumulative distribution function.

Returns the value of the cumulative distribution function of the F-distribution, also known as Snedecor’s F-distribution or the Fisher-Snedecor distribution.

The F-distribution with parameters $$d_n$$ and $$d_d$$ is the distribution of the random variable,

$X = \frac{U_n/d_n}{U_d/d_d},$

where $$U_n$$ and $$U_d$$ are random variables distributed $$\chi^2$$, with $$d_n$$ and $$d_d$$ degrees of freedom, respectively.

Parameters:
dfnarray_like

First parameter (positive float).

dfdarray_like

Second parameter (positive float).

xarray_like

Argument (nonnegative float).

outndarray, optional

Optional output array for the function values

Returns:
yscalar or ndarray

The CDF of the F-distribution with parameters dfn and dfd at x.

Notes

The regularized incomplete beta function is used, according to the formula,

$F(d_n, d_d; x) = I_{xd_n/(d_d + xd_n)}(d_n/2, d_d/2).$

Wrapper for the Cephes [1] routine fdtr.

References

[1]

Cephes Mathematical Functions Library, http://www.netlib.org/cephes/