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

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 [R433] Fortran routine cdfbet.

The cumulative distribution function p is computed using a routine by DiDinato and Morris [R434]. 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

 [R433] (1, 2) Barry Brown, James Lovato, and Kathy Russell, CDFLIB: Library of Fortran Routines for Cumulative Distribution Functions, Inverses, and Other Parameters.
 [R434] (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.

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