scipy.special.btdtr

scipy.special.btdtr(a, b, x) = <ufunc 'btdtr'>

Cumulative density function of the beta distribution.

Returns the integral from zero to x of the beta probability density function,

\[I = \int_0^x \frac{\Gamma(a + b)}{\Gamma(a)\Gamma(b)} t^{a-1} (1-t)^{b-1}\,dt\]

where \(\Gamma\) is the gamma function.

Parameters:

a : array_like

Shape parameter (a > 0).

b : array_like

Shape parameter (b > 0).

x : array_like

Upper limit of integration, in [0, 1].

Returns:

I : ndarray

Cumulative density function of the beta distribution with parameters a and b at x.

See also

betainc

Notes

This function is identical to the incomplete beta integral function betainc.

Wrapper for the Cephes [R328] routine btdtr.

References

[R328]

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