Class Beta

java.lang.Object
smile.math.special.Beta

public class Beta extends Object
The beta function, also called the Euler integral of the first kind.

B(x, y) = 01 tx-1 (1-t)y-1dt

for x, y > 0 and the integration is over [0, 1]. The beta function is symmetric, i.e. B(x, y) = B(y, x).

  • Method Details

    • beta

      public static double beta(double x, double y)
      Beta function, also called the Euler integral of the first kind. The beta function is symmetric, i.e. B(x,y)==B(y,x).
      Parameters:
      x - x > 0
      y - y > 0
      Returns:
      the function value.
    • regularizedIncompleteBetaFunction

      public static double regularizedIncompleteBetaFunction(double alpha, double beta, double x)
      Regularized Incomplete Beta function. The regularized incomplete beta function is the cumulative distribution function of the beta distribution, and is related to the cumulative distribution function of a random variable X following a binomial distribution.

      The implementation employs the continued fraction approximation (see Numerical Recipes).

      Parameters:
      alpha - alpha > 0
      beta - beta > 0
      x - x > 0
      Returns:
      the function value.
    • inverseRegularizedIncompleteBetaFunction

      public static double inverseRegularizedIncompleteBetaFunction(double alpha, double beta, double p)
      Inverse of regularized incomplete beta function.
      Parameters:
      alpha - alpha > 0
      beta - beta > 0
      p - 0 <= p <= 1
      Returns:
      the function value.