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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=x0Γ(a+b)Γ(a)Γ(b)ta1(1t)b1dt

where Γ 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

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