Loading [MathJax]/jax/output/HTML-CSS/jax.js
SciPy

This is documentation for an old release of SciPy (version 0.18.1). Read this page in the documentation of the latest stable release (version 1.15.1).

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=x0Γ(a+b)Γ(a)Γ(b)ta1(1t)b1dt
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.

Previous topic

scipy.special.btdtria

Next topic

scipy.special.fdtr