scipy.special.btdtrib¶
- scipy.special.btdtrib(a, p, x) = <ufunc 'btdtrib'>¶
Inverse of
btdtrwith 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
- aarray_like
Shape parameter (a > 0).
- parray_like
Cumulative probability, in [0, 1].
- xarray_like
The quantile, in [0, 1].
- Returns
- bndarray
The value of the shape parameter b such that btdtr(a, b, x) = p.
See also
Notes
Wrapper for the CDFLIB [1] Fortran routine cdfbet.
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., Algorithm 708: Significant Digit Computation of the Incomplete Beta Function Ratios. ACM Trans. Math. Softw. 18 (1993), 360-373.