/// <inheritdoc /> public override double LeftProbability(double x) { if (x <= 0.0) { return(0.0); } else { double p = nu1 * x; double q = nu2 + p; double y = p / q; return(beta.LeftProbability(y)); } }
/// <inheritdoc /> public override double LeftProbability(double x) { if (x <= 0.0) { return(0.0); } else { double p = nu1 * x; double q = nu2 + p; double y = p / q; return(beta.LeftProbability(y)); //return (AdvancedMath.Beta(nu1 / 2.0, nu2 / 2.0, nu1 * x / (nu2 + nu1 * x)) / AdvancedMath.Beta(0.5 * nu1, 0.5 * nu2)); } }
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 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); }