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# scipy.special.btdtri

scipy.special.btdtri(a, b, p, out=None)

  The p-th quantile of the beta distribution.

  This function is the inverse of the beta cumulative distribution function, `btdtr`, returning the value of x for which btdtr(a, b, x) = p, or

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

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

  Parameters:
    a array_like

      Shape parameter (a > 0).

    b array_like

      Shape parameter (b > 0).

    p array_like

      Cumulative probability, in [0, 1].

    out ndarray, optional

      Optional output array for the function values

  Returns:
    x scalar or ndarray

      The quantile corresponding to p.

  See also

  `betaincinv`
  `btdtr`

  Notes

  The value of x is found by interval halving or Newton iterations.

  Wrapper for the Cephes [1] routine incbi, which solves the equivalent problem of finding the inverse of the incomplete beta integral.

  References

  [1]

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