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);
}
}
}