scipy.special.btdtrib

scipy.special.btdtrib(a, p, x) = <ufunc 'btdtrib'>

Inverse of btdtr with respect to b.

This is the inverse of the beta cumulative distribution function, btdtr, considered as a function of b, returning the value of b 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:

a : array_like

Shape parameter (a > 0).

p : array_like

Cumulative probability, in [0, 1].

x : array_like

The quantile, in [0, 1].

Returns:

b : ndarray

The value of the shape parameter b such that btdtr(a, b, x) = p.

See also

btdtr

Cumulative density function of the beta distribution.

btdtri

Inverse with respect to x.

btdtria

Inverse with respect to a.

Notes

Wrapper for the CDFLIB [R332] Fortran routine cdfbet.

The cumulative distribution function p is computed using a routine by DiDinato and Morris [R333]. Computation of b involves a seach for a value that produces the desired value of p. The search relies on the monotinicity of p with b.

References

[R332]

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

[R333]

(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.