regularizedBeta() - x near 0 or x near 1

axelclk · December 5, 2020, 6:43am

For the cases where x is “nearly equal” 0 or x is “nearly equal” 1.
Can the regularizedBeta() implementation be calculated instead of returning NaN?

github.com

Hipparchus-Math/hipparchus/blob/2f4c5c2768183291f2f62b09113a42632fe8a14f/hipparchus-core/src/main/java/org/hipparchus/special/Beta.java#L185


 * @param a Parameter {@code a}.
 * @param b Parameter {@code b}.
 * @param epsilon When the absolute value of the nth item in the
 * series is less than epsilon the approximation ceases to calculate
 * further elements in the series.
 * @param maxIterations Maximum number of "iterations" to complete.
 * @return the regularized beta function I(x, a, b)
 * @throws org.hipparchus.exception.MathIllegalStateException
 * if the algorithm fails to converge.
 */
public static double regularizedBeta(double x,
                                     final double a, final double b,
                                     double epsilon, int maxIterations) {
    double ret;
    if (Double.isNaN(x) ||
        Double.isNaN(a) ||
        Double.isNaN(b) ||
        x < 0 ||
        x > 1 ||
        a <= 0 ||

public static void test( ) {
    double t =
        org.hipparchus.special.Beta.regularizedBeta(
            1.0000001, 1.0, 1.0, DEFAULT_EPSILON, MAX_ITERATIONS);
    System.out.println(t);
  }

In this implementation 0 or 1 will be returned: