/// <inheritdoc />
public override double InverseLeftProbability(double P)
{
if ((P < 0.0) || (P > 1.0))
{
throw new ArgumentOutOfRangeException(nameof(P));
}
BetaDistribution b = new BetaDistribution(nu / 2.0, 1.0 / 2.0);
if (P <= 0.5)
{
double x = b.InverseLeftProbability(2.0 * P);
return(-Math.Sqrt(nu * (1.0 - x) / x));
}
else
{
double Q = 1.0 - P;
double x = b.InverseLeftProbability(2.0 * Q);
return(Math.Sqrt(nu * (1.0 - x) / x));
}
}
/// <inheritdoc />
public override double InverseLeftProbability(double P)
{
double y = beta.InverseLeftProbability(P);
return(nu2 / nu1 * y / (1.0 - y));
}
public void BetaInversion()
{
// test that beta distribution is accurately inverted over a wide range of a, b, P
foreach (double a in TestUtilities.GenerateRealValues(0.01, 100.0, 8)) {
foreach (double b in cs) {
BetaDistribution B = new BetaDistribution(a, b);
foreach (double P in probabilities) {
Console.WriteLine("a={0} b={1} P={2}", a, b, P);
double x = B.InverseLeftProbability(P);
Console.WriteLine(" x={0} P(x)={1}", x, B.LeftProbability(x));
// we would like to test that P(x) = P, but floating point limitations prevent us from meeting this standard
// P(x) changes so fast at extremes that sometimes even the minimal change in x causes a change
// in P(x) larger than our target precision; so instead we test that our routine gets us
// as close as it can, by checking that P(x-e) < P < P(x+e)
double Px = B.LeftProbability(x);
double Pxm = B.LeftProbability(Math.Min(0.0, x * (1.0 - TestUtilities.TargetPrecision)));
double Pxp = B.LeftProbability(Math.Max(x * (1.0 + TestUtilities.TargetPrecision), 1.0));
Assert.IsTrue((Pxm <= P) && (P <= Pxp));
}
}
}
}
public void Repro()
{
double I = 0.9998063099306;
double a = 0.00034509911609819255;
double b = 6.8453983996634218;
var bd = new BetaDistribution(a, b);
double x = bd.InverseLeftProbability(I);
Console.WriteLine(x);
Console.WriteLine(bd.LeftProbability(x));
Console.WriteLine(I);
}
public void BetaExercise()
{
double[] c = new double[] { 1.0 / 32768.0, 1.0 / 1024.0, 1.0 / 64.0, 1.0 / 8.0, 1.0 / 2.0, 1.0, 2.0, 8.0, 64.0, 1024.0, 32768.0 };
double[] p = new double[] { 1.0 / 65536.0, 1.0 / 256.0, 1.0 / 16.0, 1.0 / 4.0, 1.0 - 1.0 / 4.0, 1.0 - 1.0 / 16.0, 1.0 - 1.0 / 256.0 };
Stopwatch s = Stopwatch.StartNew();
double sum = 0.0;
foreach (double a in c) {
foreach (double b in c) {
BetaDistribution BD = new BetaDistribution(a, b);
foreach (double x in p) {
//Console.WriteLine("a={0} b={1} P={2}", a, b, x);
//Console.WriteLine(BD.InverseLeftProbability(x));
sum += BD.InverseLeftProbability(x);
}
}
}
s.Stop();
Console.WriteLine(sum);
Console.WriteLine(s.ElapsedMilliseconds);
}
public void Bug7684()
{
// These values caused incomplete Beta to be called with argument outside the interval [0,1].
double I1 = 0.9999902;
double a1 = 0.0000434313636267175;
double b1 = 18474.36071078790000;
BetaDistribution D1 = new BetaDistribution(a1, b1);
double x1 = D1.InverseLeftProbability(I1);
Console.WriteLine("{0} {1} {2}", x1, D1.LeftProbability(x1), I1);
double I2 = 0.9998063099306;
double a2 = 0.00034509911609819255;
double b2 = 6.8453983996634218;
BetaDistribution D2 = new BetaDistribution(a2, b2);
double x2 = D2.InverseLeftProbability(I2);
Console.WriteLine("{0} {1} {2}", x2, D2.LeftProbability(x2), I2);
}
/// <inheritdoc />
public override double InverseLeftProbability(double P)
{
if ((P < 0.0) || (P > 1.0)) throw new ArgumentOutOfRangeException("P");
BetaDistribution b = new BetaDistribution(nu / 2.0, 1.0 / 2.0);
if (P <= 0.5) {
double x = b.InverseLeftProbability(2.0 * P);
return (-Math.Sqrt(nu * (1.0 - x) / x));
} else {
double Q = 1.0 - P;
double x = b.InverseLeftProbability(2.0 * Q);
return (Math.Sqrt(nu * (1.0 - x) / x));
}
}