// v1 is unit normal
// v2 is normal with mean = 0, sd = 2
// v3 is gamma-normal with dof=2, mean = 0.
SchemaSampler s = new SchemaSampler(Resources.asCharSource(Resources.getResource("schema015.json"), Charsets.UTF_8).read());
TDigest tdG1 = new AVLTreeDigest(500);
TDigest tdG2 = new AVLTreeDigest(500);
TDigest td1 = new AVLTreeDigest(500);
TDigest td2 = new AVLTreeDigest(500);
TDigest td3 = new AVLTreeDigest(500);
double x1 = 0;
double x2 = 0;
double x3 = 0;
for (int i = 0; i < 1000000; i++) {
JsonNode r = s.sample();
tdG1.add(r.get("g1").asDouble());
tdG2.add(r.get("g2").asDouble());
double step1 = r.get("v1").get("step").asDouble();
td1.add(step1);
x1 += step1;
assertEquals(x1, r.get("v1").get("value").asDouble(), 0);
assertEquals(x1, r.get("v1-bare").asDouble(), 0);
double step2 = r.get("v2").get("step").asDouble();
td2.add(step2);
x2 += step2;
assertEquals(x2, r.get("v2").get("value").asDouble(), 0);
double step3 = r.get("v3").get("step").asDouble();
td3.add(step3);
x3 += step3;
assertEquals(x3, r.get("v3").get("value").asDouble(), 0);
}
// now compare against reference distributions to test accuracy of the observed step distributions
NormalDistribution normalDistribution = new NormalDistribution();
GammaDistribution gd1 = new GammaDistribution(0.2, 5);
GammaDistribution gd2 = new GammaDistribution(1, 1);
TDistribution tDistribution = new TDistribution(2);
for (double q : new double[]{0.001, 0.01, 0.1, 0.2, 0.5, 0.8, 0.9, 0.99, 0.99}) {
double uG1 = gd1.cumulativeProbability(tdG1.quantile(q));
assertEquals(q, uG1, (1 - q) * q * 10e-2);
double uG2 = gd2.cumulativeProbability(tdG2.quantile(q));
assertEquals(q, uG2, (1 - q) * q * 10e-2);
double u1 = normalDistribution.cumulativeProbability(td1.quantile(q));
assertEquals(q, u1, (1 - q) * q * 10e-2);
double u2 = normalDistribution.cumulativeProbability(td2.quantile(q) / 2);
assertEquals(q, u2, (1 - q) * q * 10e-2);
double u3 = tDistribution.cumulativeProbability(td3.quantile(q));
assertEquals(q, u3, (1 - q) * q * 10e-2);
}
}