How to use

regularizedBeta

method

in

org.apache.commons.math3.special.Beta

/** {@inheritDoc} */
public double cumulativeProbability(double x)  {
  if (x <= 0) {
    return 0;
  } else if (x >= 1) {
    return 1;
  } else {
    return Beta.regularizedBeta(x, alpha, beta);
  }
}

@Override
public double cumulativeProbability(double x) {
  double ret;
  if (x < 0) {
    ret = 0.0D;
  } else if (x >= this.numberOfTrials) {
    ret = 1.0D;
  } else {
    ret = 1.0D - Beta.regularizedBeta(this.probabilityOfSuccess, x + 1.0D, (this.numberOfTrials - x));
  }
  return ret;
}

/** {@inheritDoc} */
public double cumulativeProbability(int x) {
  double ret;
  if (x < 0) {
    ret = 0.0;
  } else {
    ret = Beta.regularizedBeta(probabilityOfSuccess,
        numberOfSuccesses, x + 1.0);
  }
  return ret;
}

/** {@inheritDoc} */
public double cumulativeProbability(int x) {
  double ret;
  if (x < 0) {
    ret = 0.0;
  } else if (x >= numberOfTrials) {
    ret = 1.0;
  } else {
    ret = 1.0 - Beta.regularizedBeta(probabilityOfSuccess,
        x + 1.0, numberOfTrials - x);
  }
  return ret;
}

/**
 * {@inheritDoc}
 */
public double cumulativeProbability(int x) {
  double ret;
  if (x < 0) {
    ret = 0.0;
  } else if (x >= numberOfTrials) {
    ret = 1.0;
  } else {
    ret = 1.0 - Beta.regularizedBeta(probabilityOfSuccess, x + 1.0, numberOfTrials - x);
  }
  return ret;
}

/**
 * Returns the
 * <a href="http://mathworld.wolfram.com/RegularizedBetaFunction.html">
 * regularized beta function</a> I(x, a, b).
 *
 * @param x Value.
 * @param a Parameter {@code a}.
 * @param b Parameter {@code b}.
 * @return the regularized beta function I(x, a, b).
 * @throws org.apache.commons.math3.exception.MaxCountExceededException
 * if the algorithm fails to converge.
 */
public static double regularizedBeta(double x, double a, double b) {
  return regularizedBeta(x, a, b, DEFAULT_EPSILON, Integer.MAX_VALUE);
}

/**
 * Returns the regularized beta function I(x, a, b).
 *
 * @param x the value.
 * @param a Parameter {@code a}.
 * @param b Parameter {@code b}.
 * @param maxIterations Maximum number of "iterations" to complete.
 * @return the regularized beta function I(x, a, b)
 * @throws org.apache.commons.math3.exception.MaxCountExceededException
 * if the algorithm fails to converge.
 */
public static double regularizedBeta(double x,
                   double a, double b,
                   int maxIterations) {
  return regularizedBeta(x, a, b, DEFAULT_EPSILON, maxIterations);
}

/**
 * Returns the
 * <a href="http://mathworld.wolfram.com/RegularizedBetaFunction.html">
 * regularized beta function</a> I(x, a, b).
 *
 * @param x Value.
 * @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.
 * @return the regularized beta function I(x, a, b)
 * @throws org.apache.commons.math3.exception.MaxCountExceededException
 * if the algorithm fails to converge.
 */
public static double regularizedBeta(double x,
                   double a, double b,
                   double epsilon) {
  return regularizedBeta(x, a, b, epsilon, Integer.MAX_VALUE);
}

/** {@inheritDoc} */
public double cumulativeProbability(double x) {
  double ret;
  if (x == 0) {
    ret = 0.5;
  } else {
    double t =
      Beta.regularizedBeta(
        degreesOfFreedom / (degreesOfFreedom + (x * x)),
        0.5 * degreesOfFreedom,
        0.5);
    if (x < 0.0) {
      ret = 0.5 * t;
    } else {
      ret = 1.0 - 0.5 * t;
    }
  }
  return ret;
}

/**
 * {@inheritDoc}
 *
 * The implementation of this method is based on
 * <ul>
 *  <li>
 *   <a href="http://mathworld.wolfram.com/F-Distribution.html">
 *   F-Distribution</a>, equation (4).
 *  </li>
 * </ul>
 */
public double cumulativeProbability(double x)  {
  double ret;
  if (x <= 0) {
    ret = 0;
  } else {
    double n = numeratorDegreesOfFreedom;
    double m = denominatorDegreesOfFreedom;
    ret = Beta.regularizedBeta((n * x) / (m + n * x),
      0.5 * n,
      0.5 * m);
  }
  return ret;
}

} else if (x > (a + 1) / (2 + b + a) &&
      1 - x <= (b + 1) / (2 + b + a)) {
  ret = 1 - regularizedBeta(1 - x, b, a, epsilon, maxIterations);
} else {
  ContinuedFraction fraction = new ContinuedFraction() {

/** {@inheritDoc} */
public double cumulativeProbability(int x) {
  double ret;
  if (x < 0) {
    ret = 0.0;
  } else {
    ret = Beta.regularizedBeta(probabilityOfSuccess,
        numberOfSuccesses, x + 1.0);
  }
  return ret;
}

/** {@inheritDoc} */
public double cumulativeProbability(double x)  {
  if (x <= 0) {
    return 0;
  } else if (x >= 1) {
    return 1;
  } else {
    return Beta.regularizedBeta(x, alpha, beta);
  }
}

/** {@inheritDoc} */
public double cumulativeProbability(int x) {
  double ret;
  if (x < 0) {
    ret = 0.0;
  } else if (x >= numberOfTrials) {
    ret = 1.0;
  } else {
    ret = 1.0 - Beta.regularizedBeta(probabilityOfSuccess,
        x + 1.0, numberOfTrials - x);
  }
  return ret;
}

/** {@inheritDoc} */
public double cumulativeProbability(int x) {
  double ret;
  if (x < 0) {
    ret = 0.0;
  } else if (x >= numberOfTrials) {
    ret = 1.0;
  } else {
    ret = 1.0 - Beta.regularizedBeta(probabilityOfSuccess,
        x + 1.0, numberOfTrials - x);
  }
  return ret;
}

/** {@inheritDoc} */
public double cumulativeProbability(int x) {
  double ret;
  if (x < 0) {
    ret = 0.0;
  } else {
    ret = Beta.regularizedBeta(probabilityOfSuccess,
        numberOfSuccesses, x + 1.0);
  }
  return ret;
}

/** {@inheritDoc} */
public double cumulativeProbability(double x)  {
  if (x <= 0) {
    return 0;
  } else if (x >= 1) {
    return 1;
  } else {
    return Beta.regularizedBeta(x, alpha, beta);
  }
}

@Override
public double cumulativeProbability(double x) {
  double ret;
  if (x < 0) {
    ret = 0.0D;
  } else if (x >= this.numberOfTrials) {
    ret = 1.0D;
  } else {
    ret = 1.0D - Beta.regularizedBeta(this.probabilityOfSuccess, x + 1.0D, (this.numberOfTrials - x));
  }
  return ret;
}

/**
 * Returns the
 * <a href="http://mathworld.wolfram.com/RegularizedBetaFunction.html">
 * regularized beta function</a> I(x, a, b).
 *
 * @param x Value.
 * @param a Parameter {@code a}.
 * @param b Parameter {@code b}.
 * @return the regularized beta function I(x, a, b).
 * @throws org.apache.commons.math3.exception.MaxCountExceededException
 * if the algorithm fails to converge.
 */
public static double regularizedBeta(double x, double a, double b) {
  return regularizedBeta(x, a, b, DEFAULT_EPSILON, Integer.MAX_VALUE);
}

/**
 * Returns the regularized beta function I(x, a, b).
 *
 * @param x the value.
 * @param a Parameter {@code a}.
 * @param b Parameter {@code b}.
 * @param maxIterations Maximum number of "iterations" to complete.
 * @return the regularized beta function I(x, a, b)
 * @throws org.apache.commons.math3.exception.MaxCountExceededException
 * if the algorithm fails to converge.
 */
public static double regularizedBeta(double x,
                   double a, double b,
                   int maxIterations) {
  return regularizedBeta(x, a, b, DEFAULT_EPSILON, maxIterations);
}