#### Previous topic

scipy.special.btdtri

#### Next topic

scipy.special.btdtrib

# scipy.special.btdtria

`scipy.special.``btdtria`(p, b, x) = <ufunc 'btdtria'>

  Inverse of `btdtr` with respect to a.

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

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

  Parameters: | p : array_like Cumulative probability, in [0, 1]. b : array_like Shape parameter (b > 0). x : array_like The quantile, in [0, 1].
  Returns: | a : ndarray The value of the shape parameter a such that btdtr(a, b, x) = p.

  See also

  `btdtr`
    Cumulative density function of the beta distribution.
  `btdtri`
    Inverse with respect to x.
  `btdtrib`
    Inverse with respect to b.

  Notes

  Wrapper for the CDFLIB [R386] Fortran routine cdfbet.

  The cumulative distribution function p is computed using a routine by DiDinato and Morris [R387]. Computation of a involves a seach for a value that produces the desired value of p. The search relies on the monotinicity of p with a.

  References

  [R386] | (1, 2) Barry Brown, James Lovato, and Kathy Russell, CDFLIB: Library of Fortran Routines for Cumulative Distribution Functions, Inverses, and Other Parameters.

  [R387] | (1, 2) DiDinato, A. R. and Morris, A. H., Algorithm 708: Significant Digit Computation of the Incomplete Beta Function Ratios. ACM Trans. Math. Softw. 18 (1993), 360-373.