scipy.special.btdtr

scipy.special.btdtr(a, b, x, out=None)

Cumulative distribution 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.

Deprecated since version 1.12.0: This function is deprecated and will be removed from SciPy 1.14.0. Use scipy.special.betainc instead.

Parameters:

aarray_like

Shape parameter (a > 0).

barray_like

Shape parameter (b > 0).

xarray_like

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

outndarray, optional

Optional output array for the function values

Returns:

Iscalar or ndarray

Cumulative distribution 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 [1] routine btdtr.

References

[1]

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