protected void assertCDF(
final double[] p, final double[] x, final ProbabilityDistribution<Double> dist) {
assertCDFWithNull(dist);
for (int i = 0; i < p.length; i++) {
assertEquals(dist.getCDF(x[i]), p[i], EPS);
}
}
protected void assertCDFWithNull(final ProbabilityDistribution<Double> dist) {
try {
dist.getCDF(null);
Assert.fail();
} catch (final IllegalArgumentException e) {
// Expected
}
}
@Test
public void test() {
double x;
final double eps = 1e-5;
for (int i = 0; i < 100; i++) {
x = RANDOM.nextDouble();
assertEquals(x, F.evaluate(T.getCDF(x)), eps);
}
}
protected void assertInverseCDF(final double[] x, final ProbabilityDistribution<Double> dist) {
assertInverseCDFWithNull(dist);
for (final double d : x) {
assertEquals(dist.getInverseCDF(dist.getCDF(d)), d, EPS);
}
try {
dist.getInverseCDF(3.4);
Assert.fail();
} catch (final IllegalArgumentException e) {
// Expected
}
try {
dist.getInverseCDF(-0.2);
Assert.fail();
} catch (final IllegalArgumentException e) {
// Expected
}
}
/**
* @param x The parameters for the function, $(x, y, \rho$, with $-1 \geq \rho \geq 1$, not null
* @return The cdf
*/
@Override
public double getCDF(final double[] x) {
Validate.notNull(x);
Validate.isTrue(x.length == 3, "Need a, b and rho values");
Validate.isTrue(x[2] >= -1 && x[2] <= 1, "Correlation must be >= -1 and <= 1");
final double a = x[0];
double b = x[1];
final double rho = x[2];
if (a == Double.POSITIVE_INFINITY || b == Double.POSITIVE_INFINITY) {
return 1;
}
if (a == Double.NEGATIVE_INFINITY || b == Double.NEGATIVE_INFINITY) {
return 0;
}
final double sumSq = (a * a + b * b) / 2.;
double rho1, rho2, rho3, ab, absDiff, h5, c, d, mult = 0, rho3Sq, eab, e, result;
if (Math.abs(rho) >= 0.7) {
rho1 = 1 - rho * rho;
rho2 = Math.sqrt(rho1);
if (rho < 0) {
b *= -1;
}
ab = a * b;
eab = Math.exp(-ab / 2.);
if (Math.abs(rho) < 1) {
absDiff = Math.abs(a - b);
h5 = absDiff * absDiff / 2.;
absDiff = absDiff / rho2;
c = 0.5 - ab / 8.;
d = 3. - 2. * c * h5;
mult =
0.13298076 * absDiff * d * (1 - NORMAL.getCDF(absDiff))
- Math.exp(-h5 / rho1) * (d + c * rho1) * 0.053051647;
for (int i = 0; i < 5; i++) {
rho3 = rho2 * X[i];
rho3Sq = rho3 * rho3;
rho1 = Math.sqrt(1 - rho3Sq);
if (eab == 0) {
e = 0;
} else {
e = Math.exp(-ab / (1 + rho1)) / rho1 / eab;
}
mult = mult - Y[i] * Math.exp(-h5 / rho3Sq) * (e - 1 - c * rho3Sq);
}
}
final double corr = Double.isNaN(mult) ? 0. : mult * rho2 * eab;
result = corr + NORMAL.getCDF(Math.min(a, b));
if (rho < 0) {
result = NORMAL.getCDF(a) - result;
}
return result;
}
ab = a * b;
if (rho != 0) {
for (int i = 0; i < 5; i++) {
rho3 = rho * X[i];
rho1 = 1 - rho3 * rho3;
mult = mult + Y[i] * Math.exp((rho3 * ab - sumSq) / rho1) / Math.sqrt(rho1);
}
}
final double corr = Double.isNaN(mult) ? 0. : rho * mult;
return NORMAL.getCDF(a) * NORMAL.getCDF(b) + corr;
}