Method lnBeta

JSAT/src/jsat/math/SpecialMath.java:539–555

(double z, double w)

    }
    
    public static double lnBeta(double z, double w)
    {
        /*
         * The beta function is defined by
         *
         *           Gamma(z) Gamma(w)
         * B(z, w) = -----------------
         *             Gamma(z + w)
         *
         * However, the definition is numericaly unstable (large value / large value to small result & small input).
         * Taking the log of each size and then exponentiating gives a more stable method of computing the result
         *
         *            lnGamma(z) + lnGamma(w) - lnGamma(z + w)
         * B(z, w) = e
         */
        return lnGamma(z)+lnGamma(w)-lnGamma(z+w);
    }
    
    /**
     * Computes the regularized incomplete beta function, I<sub>x</sub>(a, b). The result of which is always in the range [0, 1]