| public InverseDistributionFunction ( double p ) : double | ||
| p | double | |
| return | double | |
public void ConstructorTest()
{
var t = new TDistribution(degreesOfFreedom: 4.2);
double mean = t.Mean; // 0.0
double median = t.Median; // 0.0
double var = t.Variance; // 1.9090909090909089
double cdf = t.DistributionFunction(x: 1.4); // 0.88456136730659074
double pdf = t.ProbabilityDensityFunction(x: 1.4); // 0.13894002185341031
double lpdf = t.LogProbabilityDensityFunction(x: 1.4); // -1.9737129364307417
double ccdf = t.ComplementaryDistributionFunction(x: 1.4); // 0.11543863269340926
double icdf = t.InverseDistributionFunction(p: cdf); // 1.4000000000000012
double hf = t.HazardFunction(x: 1.4); // 1.2035833984833988
double chf = t.CumulativeHazardFunction(x: 1.4); // 2.1590162088918525
string str = t.ToString(CultureInfo.InvariantCulture); // T(x; df = 4.2)
Assert.AreEqual(0.0, mean);
Assert.AreEqual(0.0, median);
Assert.AreEqual(1.9090909090909089, var);
Assert.AreEqual(2.1590162088918525, chf);
Assert.AreEqual(0.88456136730659074, cdf);
Assert.AreEqual(0.13894002185341031, pdf);
Assert.AreEqual(-1.9737129364307417, lpdf);
Assert.AreEqual(1.2035833984833988, hf);
Assert.AreEqual(0.11543863269340926, ccdf);
Assert.AreEqual(1.4000000000000012, icdf);
Assert.AreEqual("T(x; df = 4.2)", str);
}
/// <summary>
/// Gets the inverse of the cumulative distribution function (icdf) for
/// this distribution evaluated at probability <c>p</c>. This function
/// is also known as the Quantile function.
/// </summary>
/// <param name="p">A probability value between 0 and 1.</param>
/// <returns>A sample which could original the given probability
/// value when applied in the <see cref="UnivariateContinuousDistribution.DistributionFunction(double)" />.</returns>
/// <remarks>The Inverse Cumulative Distribution Function (ICDF) specifies, for
/// a given probability, the value which the random variable will be at,
/// or below, with that probability.</remarks>
protected internal override double InnerInverseDistributionFunction(double p)
{
// https://www.wolframalpha.com/input/?i=sqrt((N+*(+N-+2)*x%C2%B2)+%2F+((N-1)%C2%B2+-+N*x%C2%B2))+%3D+t+solve+for+x
double N = NumberOfSamples;
double t = tDistribution.InverseDistributionFunction((1 - p) / N);
double a = (N - 1.0) / Math.Sqrt(N);
double b = Math.Sqrt((t * t) / (N + t * t - 2));
double r = a * b;
return(r);
}
/// <summary>
/// Computes the power for a test with givens values of
/// <see cref="IPowerAnalysis.Effect">effect size</see> and <see cref="IPowerAnalysis.Samples">
/// number of samples</see> under <see cref="IPowerAnalysis.Size"/>.
/// </summary>
///
/// <returns>
/// The power for the test under the given conditions.
/// </returns>
///
public override void ComputePower()
{
double delta = Effect * Math.Sqrt(Samples);
double df = (Samples - 1);
TDistribution td = new TDistribution(df);
NoncentralTDistribution nt = new NoncentralTDistribution(df, delta);
switch (Tail)
{
case DistributionTail.TwoTail:
{
double Ta = td.InverseDistributionFunction(1.0 - Size / 2);
double pa = nt.ComplementaryDistributionFunction(+Ta);
double pb = nt.DistributionFunction(-Ta);
Power = pa + pb;
break;
}
case DistributionTail.OneLower:
{
double Ta = td.InverseDistributionFunction(Size);
Power = nt.DistributionFunction(Ta);
break;
}
case DistributionTail.OneUpper:
{
double Ta = td.InverseDistributionFunction(1.0 - Size);
Power = nt.ComplementaryDistributionFunction(Ta);
break;
}
default:
throw new InvalidOperationException();
}
}
public void MedianTest()
{
TDistribution target = new TDistribution(7.6);
Assert.AreEqual(target.Median, target.InverseDistributionFunction(0.5));
}
public void InverseDistributionFunctionLeftTailTest()
{
double[] a = { 0.1, 0.05, 0.025, 0.01, 0.005, 0.001, 0.0005 };
double[,] expected =
{
{ 1, 3.078, 6.314, 12.706, 31.821, 63.656, 318.289, 636.578 },
{ 2, 1.886, 2.920, 4.303, 6.965, 9.925, 22.328, 31.600 },
{ 3, 1.638, 2.353, 3.182, 4.541, 5.841, 10.214, 12.924 },
{ 4, 1.533, 2.132, 2.776, 3.747, 4.604, 7.173, 8.610 },
{ 5, 1.476, 2.015, 2.571, 3.365, 4.032, 5.894, 6.869 },
{ 6, 1.440, 1.943, 2.447, 3.143, 3.707, 5.208, 5.959 },
{ 7, 1.415, 1.895, 2.365, 2.998, 3.499, 4.785, 5.408 },
{ 8, 1.397, 1.860, 2.306, 2.896, 3.355, 4.501, 5.041 },
{ 9, 1.383, 1.833, 2.262, 2.821, 3.250, 4.297, 4.781 },
{ 10, 1.372, 1.812, 2.228, 2.764, 3.169, 4.144, 4.587 },
{ 11, 1.363, 1.796, 2.201, 2.718, 3.106, 4.025, 4.437 },
{ 12, 1.356, 1.782, 2.179, 2.681, 3.055, 3.930, 4.318 },
{ 13, 1.350, 1.771, 2.160, 2.650, 3.012, 3.852, 4.221 },
{ 14, 1.345, 1.761, 2.145, 2.624, 2.977, 3.787, 4.140 },
{ 15, 1.341, 1.753, 2.131, 2.602, 2.947, 3.733, 4.073 },
{ 16, 1.337, 1.746, 2.120, 2.583, 2.921, 3.686, 4.015 },
{ 17, 1.333, 1.740, 2.110, 2.567, 2.898, 3.646, 3.965 },
{ 18, 1.330, 1.734, 2.101, 2.552, 2.878, 3.610, 3.922 },
{ 19, 1.328, 1.729, 2.093, 2.539, 2.861, 3.579, 3.883 },
{ 20, 1.325, 1.725, 2.086, 2.528, 2.845, 3.552, 3.850 },
{ 21, 1.323, 1.721, 2.080, 2.518, 2.831, 3.527, 3.819 },
{ 22, 1.321, 1.717, 2.074, 2.508, 2.819, 3.505, 3.792 },
{ 23, 1.319, 1.714, 2.069, 2.500, 2.807, 3.485, 3.768 },
{ 24, 1.318, 1.711, 2.064, 2.492, 2.797, 3.467, 3.745 },
{ 25, 1.316, 1.708, 2.060, 2.485, 2.787, 3.450, 3.725 },
{ 26, 1.315, 1.706, 2.056, 2.479, 2.779, 3.435, 3.707 },
{ 27, 1.314, 1.703, 2.052, 2.473, 2.771, 3.421, 3.689 },
{ 28, 1.313, 1.701, 2.048, 2.467, 2.763, 3.408, 3.674 },
{ 29, 1.311, 1.699, 2.045, 2.462, 2.756, 3.396, 3.660 },
{ 30, 1.310, 1.697, 2.042, 2.457, 2.750, 3.385, 3.646 },
{ 60, 1.296, 1.671, 2.000, 2.390, 2.660, 3.232, 3.460 },
{ 120, 1.289, 1.658, 1.980, 2.358, 2.617, 3.160, 3.373 },
};
for (int i = 0; i < expected.GetLength(0); i++)
{
int df = (int)expected[i, 0];
TDistribution target = new TDistribution(df);
for (int j = 1; j < expected.GetLength(1); j++)
{
double actual = target.InverseDistributionFunction(1.0 - a[j - 1]);
Assert.IsTrue(Math.Abs(expected[i, j] / actual - 1) < 1e-3);
}
}
}
public void InverseDistributionFunctionTest2()
{
TDistribution target = new TDistribution(24);
double expected = 1.710882023;
double actual = target.InverseDistributionFunction(0.95);
Assert.AreEqual(expected, actual, 1e-06);
}
public void InverseDistributionFunctionTest()
{
TDistribution target;
double[] expected;
target = new TDistribution(1);
expected = new double[] { 6.3138, 3.0777, 1.9626, 1.3764, 1, 0.7265, 0.5095, 0.3249, 0.1584, 0 };
for (int i = 1; i <= 10; i++)
{
double percent = i / 10.0;
double actual = target.InverseDistributionFunction(1.0 - percent / 2);
Assert.AreEqual(expected[i - 1], actual, 1e-4);
Assert.IsFalse(Double.IsNaN(actual));
}
target = new TDistribution(4.2);
expected = new double[] { 2.103, 1.5192, 1.1814, 0.9358, 0.7373, 0.5664, 0.4127, 0.2699, 0.1334, 0 };
for (int i = 1; i <= 10; i++)
{
double percent = i / 10.0;
double actual = target.InverseDistributionFunction(1.0 - percent / 2);
Assert.AreEqual(expected[i - 1], actual, 1e-4);
Assert.IsFalse(Double.IsNaN(actual));
}
}
