# scipy.special.btdtr

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

  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.

  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 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/

scipy.special.bdtrin scipy.special.btdtri