Welcome

This tiny library contains some C/Cython code for calculating

• the (normalized) incomplete Beta function - betainc
• the first derivatives (w.r.t. shape parameters) of the incomplete Beta function via the INBEDER algorithm
• the digamma (Psi) function, the beta function and its logarithm (betaln)

API

• beta(p, q): Calculate the Beta function, where B(p,q) = Gamma(p)*Gamma(q)/Gamma(p+q)
• betaln(p, q): Calculate the logarithm of the Beta function, where betaln(p,q) = ln B(p,q) = ln Gamma(p) + ln Gamma(q) - ln Gamma(p+q)
• betainc(x, p, q): Calculate the regularized incomplete Beta function, where betainc(x, p, q) = I_x(p, q). See http://mathworld.wolfram.com/IncompleteBetaFunction.html
• betaincderp(x, p, q): Compute the first derivative of the regularized incomplete Beta function with respect to the first shape parameter p.
• betaincderq(x, p, q): First derivative of the regularized incomplete Beta function with respect to the second shape parameter q.
• digamma(x): The digamma function. See http://mathworld.wolfram.com/DigammaFunction.html.

Installation

$ pip install betaincder

Usage

The functions can be invoked from python, or cimported from Cython.

from betaincder import betainc, betaincderp, betaincderq
print betaincderq(.5, 10, 10)

or

%%cython 
from betaincder.c.betaincder cimport digamma, betaln, betainc, betaincderq
print betaincderq(.5, 10, 10)

References

• Robinson-Cox, J. F., & Boik, R. J. (1998). Derivatives of the Incomplete Beta Function. Journal of Statistical Software, 3(01).
• Bernardo, Jose M. "Algorithm AS 103: Psi (digamma) function." Journal of the Royal Statistical Society. Series C (Applied Statistics) 25.3 (1976): 315-317.