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# scipy.special.gdtrib

scipy.special.gdtrib(a, p, x, out=None) = <ufunc 'gdtrib'>

  Inverse of `gdtr` vs b.

  Returns the inverse with respect to the parameter b of `p = gdtr(a, b, x)`, the cumulative distribution function of the gamma distribution.

  Parameters:
    a array_like

      a parameter values of gdtr(a, b, x). 1/a is the “scale” parameter of the gamma distribution.

    p array_like

      Probability values.

    x array_like

      Nonnegative real values, from the domain of the gamma distribution.

    out ndarray, optional

      If a fourth argument is given, it must be a numpy.ndarray whose size matches the broadcast result of a, b and x. out is then the array returned by the function.

  Returns:
    b scalar or ndarray

      Values of the b parameter such that p = gdtr(a, b, x). b is the “shape” parameter of the gamma distribution.

  See also

  `gdtr`

    CDF of the gamma distribution.

  `gdtria`

    Inverse with respect to a of gdtr(a, b, x).

  `gdtrix`

    Inverse with respect to x of gdtr(a, b, x).

  Notes

  Wrapper for the CDFLIB [1] Fortran routine cdfgam.

  The cumulative distribution function p is computed using a routine by DiDinato and Morris [2]. Computation of b involves a search for a value that produces the desired value of p. The search relies on the monotonicity of p with b.

  References

  [1]

  Barry Brown, James Lovato, and Kathy Russell, CDFLIB: Library of Fortran Routines for Cumulative Distribution Functions, Inverses, and Other Parameters.

  [2]

  DiDinato, A. R. and Morris, A. H., Computation of the incomplete gamma function ratios and their inverse. ACM Trans. Math. Softw. 12 (1986), 377-393.

  Examples

  First evaluate `gdtr`.

      >>> from scipy.special import gdtr, gdtrib
      >>> p = gdtr(1.2, 3.4, 5.6)
      >>> print(p)
      0.94378087442

  Verify the inverse.

      >>> gdtrib(1.2, p, 5.6)
      3.3999999999723882