### Question:
NormalDistribution extends AbstractContinuousDistribution { @Override public double cumulativeProbability(double x) { final double dev = x - mean; if (Math.abs(dev) > 40 * standardDeviation) { return dev < 0 ? 0.0d : 1.0d; } return 0.5 * Erfc.value(-dev / (standardDeviation * SQRT2)); } NormalDistribution(double mean,
                              double sd); double getStandardDeviation(); @Override double density(double x); @Override double logDensity(double x); @Override double cumulativeProbability(double x); @Override double inverseCumulativeProbability(final double p); @Override double probability(double x0,
                              double x1); @Override double getMean(); @Override double getVariance(); @Override double getSupportLowerBound(); @Override double getSupportUpperBound(); @Override boolean isSupportConnected(); @Override ContinuousDistribution.Sampler createSampler(final UniformRandomProvider rng);  }### Answer:
@Test void testCumulativeProbability() { final ContinuousDistribution dist = new NormalDistribution(0, 1); final double x = -10; final double expected = 7.61985e-24; final double v = dist.cumulativeProbability(x); final double tol = 1e-5; Assertions.assertEquals(1, v / expected, 1e-5); }
@Test void testLowerTail() { final NormalDistribution distribution = new NormalDistribution(0, 1); for (int i = 0; i < 100; i++) { final double lowerTail = distribution.cumulativeProbability(-i); if (i < 39) { Assertions.assertTrue(lowerTail > 0); } else { Assertions.assertEquals(0, lowerTail); } } }
@Test void testUpperTail() { final NormalDistribution distribution = new NormalDistribution(0, 1); for (int i = 0; i < 100; i++) { final double upperTail = distribution.cumulativeProbability(i); if (i < 9) { Assertions.assertTrue(upperTail < 1); } else { Assertions.assertEquals(1, upperTail); } } }
@Test void testExtremeValues() { final NormalDistribution distribution = new NormalDistribution(0, 1); Assertions.assertEquals(1, distribution.cumulativeProbability(Double.MAX_VALUE)); Assertions.assertEquals(0, distribution.cumulativeProbability(-Double.MAX_VALUE)); Assertions.assertEquals(1, distribution.cumulativeProbability(Double.POSITIVE_INFINITY)); Assertions.assertEquals(0, distribution.cumulativeProbability(Double.NEGATIVE_INFINITY)); }