/// Returns the regularized beta function I(x, a, b).
///
/// The implementation of this method is based on:
/// <ul>
/// <li>
/// <a href="http://mathworld.wolfram.com/RegularizedBetaFunction.html">
/// Regularized Beta Function</a>.</li>
/// <li>
/// <a href="http://functions.wolfram.com/06.21.10.0001.01">
/// Regularized Beta Function</a>.</li>
/// </ul>
///
/// @param x the 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.
/// @param maxIterations Maximum number of "iterations" to complete.
/// @return the regularized beta function I(x, a, b)
/// @throws NReco.Math3.Exception.MaxCountExceededException
/// if the algorithm fails to converge.
public static double regularizedBeta(double x,
double a, double b,
double epsilon, int maxIterations)
{
double ret;
if (Double.IsNaN(x) ||
Double.IsNaN(a) ||
Double.IsNaN(b) ||
x < 0 ||
x > 1 ||
a <= 0 ||
b <= 0)
{
ret = Double.NaN;
}
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 BetaContinuedFraction(a, b);
ret = Math.Exp((a * MathUtil.Log(x)) + (b * MathUtil.Log1p(-x)) - //(b * Math.log1p(-x))
MathUtil.Log(a) - logBeta(a, b)) *
1.0 / fraction.evaluate(x, epsilon, maxIterations);
}
return(ret);
}
public static double regularizedBeta(double x, double a, double b, double epsilon, int maxIterations)
{
if ((((double.IsNaN(x) || double.IsNaN(a)) || (double.IsNaN(b) || (x < 0.0))) || ((x > 1.0) || (a <= 0.0))) || (b <= 0.0))
{
return(double.NaN);
}
if ((x > ((a + 1.0) / ((2.0 + b) + a))) && ((1.0 - x) <= ((b + 1.0) / ((2.0 + b) + a))))
{
return(1.0 - regularizedBeta(1.0 - x, b, a, epsilon, maxIterations));
}
ContinuedFraction fraction = new BetaContinuedFraction(a, b);
return((Math.Exp((((a * MathUtil.Log(x)) + (b * MathUtil.Log1p(-x))) - MathUtil.Log(a)) - logBeta(a, b)) * 1.0) / fraction.evaluate(x, epsilon, maxIterations));
}
/// Returns the regularized beta function I(x, a, b).
///
/// The implementation of this method is based on:
/// <ul>
/// <li>
/// <a href="http://mathworld.wolfram.com/RegularizedBetaFunction.html">
/// Regularized Beta Function</a>.</li>
/// <li>
/// <a href="http://functions.wolfram.com/06.21.10.0001.01">
/// Regularized Beta Function</a>.</li>
/// </ul>
///
/// @param x the 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.
/// @param maxIterations Maximum number of "iterations" to complete.
/// @return the regularized beta function I(x, a, b)
/// @throws NReco.Math3.Exception.MaxCountExceededException
/// if the algorithm fails to converge.
public static double regularizedBeta(double x,
double a, double b,
double epsilon, int maxIterations) {
double ret;
if (Double.IsNaN(x) ||
Double.IsNaN(a) ||
Double.IsNaN(b) ||
x < 0 ||
x > 1 ||
a <= 0 ||
b <= 0) {
ret = Double.NaN;
} 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 BetaContinuedFraction(a,b);
ret = Math.Exp((a * MathUtil.Log(x)) + (b * MathUtil.Log1p(-x)) - //(b * Math.log1p(-x))
MathUtil.Log(a) - logBeta(a, b)) *
1.0 / fraction.evaluate(x, epsilon, maxIterations);
}
return ret;
}
