public void TestSpecialFunctions_BetaRegularized()
{
// Maple: Ix := (x,a,b) -> int(t^(a-1)*(1-t)^(b-1),t=0..x)/Beta(a,b);
// Compare with Maple: "evalf(Ix(x,0.2,0.2),20);", with relative accuracy
Assert.That(Fn.BetaRegularized(0.2, 0.2, 0.0), NumericIs.AlmostEqualTo(0.0), "A1");
Assert.That(Fn.BetaRegularized(0.2, 0.2, 0.2), NumericIs.AlmostEqualTo(.39272216435257082965), "A2");
Assert.That(Fn.BetaRegularized(0.2, 0.2, 0.5), NumericIs.AlmostEqualTo(.50000000000000000000), "A3");
Assert.That(Fn.BetaRegularized(0.2, 0.2, 0.8), NumericIs.AlmostEqualTo(.60727783564742917036), "A4");
Assert.That(Fn.BetaRegularized(0.2, 0.2, 1.0), NumericIs.AlmostEqualTo(1.0000000000000000000), "A5");
// Compare with Maple: "evalf(Ix(x,0.6,1.2),20);", with relative accuracy
Assert.That(Fn.BetaRegularized(0.6, 1.2, 0.0), NumericIs.AlmostEqualTo(0.0), "B1");
Assert.That(Fn.BetaRegularized(0.6, 1.2, 0.2), NumericIs.AlmostEqualTo(.42540331997033591754), "B2");
Assert.That(Fn.BetaRegularized(0.6, 1.2, 0.5), NumericIs.AlmostEqualTo(.71641011564425207256), "B3");
Assert.That(Fn.BetaRegularized(0.6, 1.2, 0.8), NumericIs.AlmostEqualTo(.91373194998181983314), "B4");
Assert.That(Fn.BetaRegularized(0.6, 1.2, 1.0), NumericIs.AlmostEqualTo(1.0000000000000000000), "B5");
// Compare with Maple: "evalf(Ix(x,7.0,1.2),20);", with relative accuracy
Assert.That(Fn.BetaRegularized(7.0, 1.2, 0.0), NumericIs.AlmostEqualTo(0.0), "C1");
Assert.That(Fn.BetaRegularized(7.0, 1.2, 0.2), NumericIs.AlmostEqualTo(.20126888449347947608e-4), "C2");
Assert.That(Fn.BetaRegularized(7.0, 1.2, 0.5), NumericIs.AlmostEqualTo(.11371092280417448678e-1), "C3");
Assert.That(Fn.BetaRegularized(7.0, 1.2, 0.7), NumericIs.AlmostEqualTo(.11102090346884848038, 1e-14), "C4");
Assert.That(Fn.BetaRegularized(7.0, 1.2, 0.8), NumericIs.AlmostEqualTo(.26774648551269072265, 1e-14), "C5");
Assert.That(Fn.BetaRegularized(7.0, 1.2, 0.9), NumericIs.AlmostEqualTo(.56477467605979107895), "C6");
Assert.That(Fn.BetaRegularized(7.0, 1.2, 0.95), NumericIs.AlmostEqualTo(.77753405618146275868), "C7");
Assert.That(Fn.BetaRegularized(7.0, 1.2, 1.0), NumericIs.AlmostEqualTo(1.0000000000000000000), "C8");
}
CumulativeDistribution(double x)
{
double xa = _alpha * x;
double m = xa / (xa + _beta);
return(Fn.BetaRegularized(0.5 * _alpha, 0.5 * _beta, m));
}
CumulativeDistribution(double x)
{
double beta = Fn.BetaRegularized(
0.5 * _degreesOfFreedom,
0.5,
_degreesOfFreedom / (_degreesOfFreedom + (x * x)));
return(0.5 + (0.5 * Math.Sign(x) * (_summand - beta)));
}
SetDistributionParameters(int degreesOfFreedom)
{
if (!IsValidParameterSet(degreesOfFreedom))
{
throw new ArgumentException(Properties.LocalStrings.ArgumentParameterSetInvalid, "degreesOfFreedom");
}
_degreesOfFreedom = degreesOfFreedom;
_chiSquareDistribution.SetDistributionParameters(degreesOfFreedom);
double a = 0.5 * (_degreesOfFreedom + 1);
double nLn = Fn.GammaLn(a);
double dLn1 = Math.Log(Math.Sqrt(Math.PI * _degreesOfFreedom));
double dLn2 = Fn.GammaLn(0.5 * _degreesOfFreedom);
_exponent = -a;
_factor = Math.Exp(nLn - dLn1 - dLn2);
_summand = Fn.BetaRegularized(0.5 * _degreesOfFreedom, 0.5, 1);
}
CumulativeDistribution(
double x
)
{
return(Fn.BetaRegularized(_alpha, _beta, x));
}
CumulativeDistribution(double x)
{
return(Fn.BetaRegularized(_n - x, x + 1, 1 - _p));
}