@Test
public void testContinuous() {
final double x0 = 0.0;
final double x1 = 1.0;
final double x2 = 2.0;
final double x3 = 3.0;
final double p12 = 0.5;
final AbstractRealDistribution distribution;
distribution =
new AbstractRealDistribution(null) {
private static final long serialVersionUID = 1L;
@Override
public double cumulativeProbability(final double x) {
if ((x < x0) || (x > x3)) {
throw new OutOfRangeException(x, x0, x3);
}
if (x <= x1) {
return p12 * (x - x0) / (x1 - x0);
} else if (x <= x2) {
return p12;
} else if (x <= x3) {
return p12 + (1.0 - p12) * (x - x2) / (x3 - x2);
}
return 0.0;
}
@Override
public double density(final double x) {
if ((x < x0) || (x > x3)) {
throw new OutOfRangeException(x, x0, x3);
}
if (x <= x1) {
return p12 / (x1 - x0);
} else if (x <= x2) {
return 0.0;
} else if (x <= x3) {
return (1.0 - p12) / (x3 - x2);
}
return 0.0;
}
@Override
public double getNumericalMean() {
return ((x0 + x1) * p12 + (x2 + x3) * (1.0 - p12)) / 2.0;
}
@Override
public double getNumericalVariance() {
final double meanX = getNumericalMean();
final double meanX2;
meanX2 =
((x0 * x0 + x0 * x1 + x1 * x1) * p12 + (x2 * x2 + x2 * x3 + x3 * x3) * (1.0 - p12))
/ 3.0;
return meanX2 - meanX * meanX;
}
@Override
public double getSupportLowerBound() {
return x0;
}
@Override
public double getSupportUpperBound() {
return x3;
}
@Override
public boolean isSupportConnected() {
return false;
}
@Override
public double probability(final double x) {
throw new UnsupportedOperationException();
}
};
final double expected = x1;
final double actual = distribution.inverseCumulativeProbability(p12);
Assert.assertEquals("", expected, actual, distribution.getSolverAbsoluteAccuracy());
}
@Test
public void testDiscontinuous() {
final double x0 = 0.0;
final double x1 = 0.25;
final double x2 = 0.5;
final double x3 = 0.75;
final double x4 = 1.0;
final double p12 = 1.0 / 3.0;
final double p23 = 2.0 / 3.0;
final AbstractRealDistribution distribution;
distribution =
new AbstractRealDistribution(null) {
private static final long serialVersionUID = 1L;
@Override
public double cumulativeProbability(final double x) {
if ((x < x0) || (x > x4)) {
throw new OutOfRangeException(x, x0, x4);
}
if (x <= x1) {
return p12 * (x - x0) / (x1 - x0);
} else if (x <= x2) {
return p12;
} else if (x <= x3) {
return p23;
} else {
return (1.0 - p23) * (x - x3) / (x4 - x3) + p23;
}
}
@Override
public double density(final double x) {
if ((x < x0) || (x > x4)) {
throw new OutOfRangeException(x, x0, x4);
}
if (x <= x1) {
return p12 / (x1 - x0);
} else if (x <= x2) {
return 0.0;
} else if (x <= x3) {
return 0.0;
} else {
return (1.0 - p23) / (x4 - x3);
}
}
@Override
public double getNumericalMean() {
final UnivariateFunction f =
new UnivariateFunction() {
public double value(final double x) {
return x * density(x);
}
};
final UnivariateIntegrator integrator = new RombergIntegrator();
return integrator.integrate(Integer.MAX_VALUE, f, x0, x4);
}
@Override
public double getNumericalVariance() {
final double meanX = getNumericalMean();
final UnivariateFunction f =
new UnivariateFunction() {
public double value(final double x) {
return x * x * density(x);
}
};
final UnivariateIntegrator integrator = new RombergIntegrator();
final double meanX2 = integrator.integrate(Integer.MAX_VALUE, f, x0, x4);
return meanX2 - meanX * meanX;
}
@Override
public double getSupportLowerBound() {
return x0;
}
@Override
public double getSupportUpperBound() {
return x4;
}
@Override
public boolean isSupportConnected() {
return false;
}
@Override
public double probability(final double x) {
throw new UnsupportedOperationException();
}
};
final double expected = x2;
final double actual = distribution.inverseCumulativeProbability(p23);
Assert.assertEquals("", expected, actual, distribution.getSolverAbsoluteAccuracy());
}