scipy.special.fdtr

scipy.special.fdtr(dfn, dfd, x) = <ufunc 'fdtr'>

F cumulative distribution function.

Returns the value of the cumulative density 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:

dfn : array_like

First parameter (positive float).

dfd : array_like

Second parameter (positive float).

x : array_like

Argument (nonnegative float).

Returns:

y : 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 [R415] routine fdtr.

References

[R415]

(1, 2) Cephes Mathematical Functions Library, http://www.netlib.org/cephes/index.html