private void checkNextUniformUniform(double min, double max) {
// Set up bin bounds - min, binBound[0], ..., binBound[binCount-2], max
final int binCount = 5;
final double binSize =
max / binCount - min / binCount; // Prevent overflow in extreme value case
final double[] binBounds = new double[binCount - 1];
binBounds[0] = min + binSize;
for (int i = 1; i < binCount - 1; i++) {
binBounds[i] = binBounds[i - 1] + binSize; // + instead of * to avoid overflow in extreme case
}
final Frequency freq = new Frequency();
for (int i = 0; i < smallSampleSize; i++) {
final double value = randomData.nextUniform(min, max);
Assert.assertTrue("nextUniform range", (value > min) && (value < max));
// Find bin
int j = 0;
while (j < binCount - 1 && value > binBounds[j]) {
j++;
}
freq.addValue(j);
}
final long[] observed = new long[binCount];
for (int i = 0; i < binCount; i++) {
observed[i] = freq.getCount(i);
}
final double[] expected = new double[binCount];
for (int i = 0; i < binCount; i++) {
expected[i] = 1d / binCount;
}
TestUtils.assertChiSquareAccept(expected, observed, 0.01);
}
/** test dispersion and failure modes for nextHex() */
@Test
@Retry(3)
public void testNextSecureHex() {
try {
randomData.nextSecureHexString(-1);
Assert.fail("negative length -- MathIllegalArgumentException expected");
} catch (MathIllegalArgumentException ex) {
// ignored
}
try {
randomData.nextSecureHexString(0);
Assert.fail("zero length -- MathIllegalArgumentException expected");
} catch (MathIllegalArgumentException ex) {
// ignored
}
String hexString = randomData.nextSecureHexString(3);
if (hexString.length() != 3) {
Assert.fail("incorrect length for generated string");
}
hexString = randomData.nextSecureHexString(1);
if (hexString.length() != 1) {
Assert.fail("incorrect length for generated string");
}
try {
hexString = randomData.nextSecureHexString(0);
Assert.fail("zero length requested -- expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// ignored
}
Frequency f = new Frequency();
for (int i = 0; i < smallSampleSize; i++) {
hexString = randomData.nextSecureHexString(100);
if (hexString.length() != 100) {
Assert.fail("incorrect length for generated string");
}
for (int j = 0; j < hexString.length(); j++) {
f.addValue(hexString.substring(j, j + 1));
}
}
double[] expected = new double[16];
long[] observed = new long[16];
for (int i = 0; i < 16; i++) {
expected[i] = (double) smallSampleSize * 100 / 16;
observed[i] = f.getCount(hex[i]);
}
TestUtils.assertChiSquareAccept(expected, observed, 0.001);
}
private void checkNextSecureIntUniform(int min, int max) {
final Frequency freq = new Frequency();
for (int i = 0; i < smallSampleSize; i++) {
final int value = randomData.nextSecureInt(min, max);
Assert.assertTrue("nextInt range", (value >= min) && (value <= max));
freq.addValue(value);
}
final int len = max - min + 1;
final long[] observed = new long[len];
for (int i = 0; i < len; i++) {
observed[i] = freq.getCount(min + i);
}
final double[] expected = new double[len];
for (int i = 0; i < len; i++) {
expected[i] = 1d / len;
}
TestUtils.assertChiSquareAccept(expected, observed, 0.0001);
}
private void checkNextLongUniform(long min, long max) {
final Frequency freq = new Frequency();
for (int i = 0; i < smallSampleSize; i++) {
final long value = randomData.nextLong(min, max);
Assert.assertTrue(
"nextLong range: " + value + " " + min + " " + max, (value >= min) && (value <= max));
freq.addValue(value);
}
final int len = ((int) (max - min)) + 1;
final long[] observed = new long[len];
for (int i = 0; i < len; i++) {
observed[i] = freq.getCount(min + i);
}
final double[] expected = new double[len];
for (int i = 0; i < len; i++) {
expected[i] = 1d / len;
}
TestUtils.assertChiSquareAccept(expected, observed, 0.01);
}
/**
* Make sure that empirical distribution of random Poisson(4)'s has P(X <= 5) close to actual
* cumulative Poisson probability and that nextPoisson fails when mean is non-positive.
*/
@Test
public void testNextPoisson() {
try {
randomData.nextPoisson(0);
Assert.fail("zero mean -- expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// ignored
}
try {
randomData.nextPoisson(-1);
Assert.fail("negative mean supplied -- MathIllegalArgumentException expected");
} catch (MathIllegalArgumentException ex) {
// ignored
}
try {
randomData.nextPoisson(0);
Assert.fail("0 mean supplied -- MathIllegalArgumentException expected");
} catch (MathIllegalArgumentException ex) {
// ignored
}
final double mean = 4.0d;
final int len = 5;
PoissonDistribution poissonDistribution = new PoissonDistribution(mean);
Frequency f = new Frequency();
randomData.reSeed(1000);
for (int i = 0; i < largeSampleSize; i++) {
f.addValue(randomData.nextPoisson(mean));
}
final long[] observed = new long[len];
for (int i = 0; i < len; i++) {
observed[i] = f.getCount(i + 1);
}
final double[] expected = new double[len];
for (int i = 0; i < len; i++) {
expected[i] = poissonDistribution.probability(i + 1) * largeSampleSize;
}
TestUtils.assertChiSquareAccept(expected, observed, 0.0001);
}
@Test
public void summarizeLSAT7dataTest() {
System.out.println("Testing summary of LSAT7 data");
readLsat7Data();
// true values from mirt package in R
String[][] trueValues = {
{"[0, 0, 0, 0, 0]", "12"},
{"[0, 0, 0, 0, 1]", "19"},
{"[0, 0, 0, 1, 0]", "1"},
{"[0, 0, 0, 1, 1]", "7"},
{"[0, 0, 1, 0, 0]", "3"},
{"[0, 0, 1, 0, 1]", "19"},
{"[0, 0, 1, 1, 0]", "3"},
{"[0, 0, 1, 1, 1]", "17"},
{"[0, 1, 0, 0, 0]", "10"},
{"[0, 1, 0, 0, 1]", "5"},
{"[0, 1, 0, 1, 0]", "3"},
{"[0, 1, 0, 1, 1]", "7"},
{"[0, 1, 1, 0, 0]", "7"},
{"[0, 1, 1, 0, 1]", "23"},
{"[0, 1, 1, 1, 0]", "8"},
{"[0, 1, 1, 1, 1]", "28"},
{"[1, 0, 0, 0, 0]", "7"},
{"[1, 0, 0, 0, 1]", "39"},
{"[1, 0, 0, 1, 0]", "11"},
{"[1, 0, 0, 1, 1]", "34"},
{"[1, 0, 1, 0, 0]", "14"},
{"[1, 0, 1, 0, 1]", "51"},
{"[1, 0, 1, 1, 0]", "15"},
{"[1, 0, 1, 1, 1]", "90"},
{"[1, 1, 0, 0, 0]", "6"},
{"[1, 1, 0, 0, 1]", "25"},
{"[1, 1, 0, 1, 0]", "7"},
{"[1, 1, 0, 1, 1]", "35"},
{"[1, 1, 1, 0, 0]", "18"},
{"[1, 1, 1, 0, 1]", "136"},
{"[1, 1, 1, 1, 0]", "32"},
{"[1, 1, 1, 1, 1]", "308"}
};
// summarize response vectors into a frequency object
Frequency freq = new Frequency();
for (int i = 0; i < lsat7.length; i++) {
freq.addValue(Arrays.toString(lsat7[i]));
}
assertEquals("Same number of response strings", trueValues.length, freq.getUniqueCount());
for (int i = 0; i < trueValues.length; i++) {
assertEquals(
"Response vector comparison: ",
Double.parseDouble(trueValues[i][1]),
Long.valueOf(freq.getCount(trueValues[i][0])).doubleValue(),
1e-5);
}
ItemResponseVector[] responseData = new ItemResponseVector[freq.getUniqueCount()];
ItemResponseVector irv = null;
Iterator<Comparable<?>> iter = freq.valuesIterator();
int index = 0;
// create array of ItemResponseVector objects
while (iter.hasNext()) {
// get response string from frequency summary and convert to byte array
Comparable<?> value = iter.next();
String s = value.toString();
s = s.substring(1, s.lastIndexOf("]"));
String[] sa = s.split(",");
byte[] rv = new byte[sa.length];
for (int i = 0; i < sa.length; i++) {
rv[i] = Byte.parseByte(sa[i].trim());
}
// create response vector objects
irv = new ItemResponseVector(rv, Long.valueOf(freq.getCount(value)).doubleValue());
responseData[index] = irv;
index++;
}
// display results of summary
for (int i = 0; i < responseData.length; i++) {
System.out.println(responseData[i].toString() + ": " + responseData[i].getFrequency());
}
}
/**
* Verifies that nextPoisson(mean) generates an empirical distribution of values consistent with
* PoissonDistributionImpl by generating 1000 values, computing a grouped frequency distribution
* of the observed values and comparing this distribution to the corresponding expected
* distribution computed using PoissonDistributionImpl. Uses ChiSquare test of goodness of fit to
* evaluate the null hypothesis that the distributions are the same. If the null hypothesis can be
* rejected with confidence 1 - alpha, the check fails.
*/
public void checkNextPoissonConsistency(double mean) {
// Generate sample values
final int sampleSize = 1000; // Number of deviates to generate
final int minExpectedCount = 7; // Minimum size of expected bin count
long maxObservedValue = 0;
final double alpha = 0.001; // Probability of false failure
Frequency frequency = new Frequency();
for (int i = 0; i < sampleSize; i++) {
long value = randomData.nextPoisson(mean);
if (value > maxObservedValue) {
maxObservedValue = value;
}
frequency.addValue(value);
}
/*
* Set up bins for chi-square test.
* Ensure expected counts are all at least minExpectedCount.
* Start with upper and lower tail bins.
* Lower bin = [0, lower); Upper bin = [upper, +inf).
*/
PoissonDistribution poissonDistribution = new PoissonDistribution(mean);
int lower = 1;
while (poissonDistribution.cumulativeProbability(lower - 1) * sampleSize < minExpectedCount) {
lower++;
}
int upper = (int) (5 * mean); // Even for mean = 1, not much mass beyond 5
while ((1 - poissonDistribution.cumulativeProbability(upper - 1)) * sampleSize
< minExpectedCount) {
upper--;
}
// Set bin width for interior bins. For poisson, only need to look at end bins.
int binWidth = 0;
boolean widthSufficient = false;
double lowerBinMass = 0;
double upperBinMass = 0;
while (!widthSufficient) {
binWidth++;
lowerBinMass = poissonDistribution.cumulativeProbability(lower - 1, lower + binWidth - 1);
upperBinMass = poissonDistribution.cumulativeProbability(upper - binWidth - 1, upper - 1);
widthSufficient = FastMath.min(lowerBinMass, upperBinMass) * sampleSize >= minExpectedCount;
}
/*
* Determine interior bin bounds. Bins are
* [1, lower = binBounds[0]), [lower, binBounds[1]), [binBounds[1], binBounds[2]), ... ,
* [binBounds[binCount - 2], upper = binBounds[binCount - 1]), [upper, +inf)
*
*/
List<Integer> binBounds = new ArrayList<Integer>();
binBounds.add(lower);
int bound = lower + binWidth;
while (bound < upper - binWidth) {
binBounds.add(bound);
bound += binWidth;
}
binBounds.add(
upper); // The size of bin [binBounds[binCount - 2], upper) satisfies binWidth <= size <
// 2*binWidth.
// Compute observed and expected bin counts
final int binCount = binBounds.size() + 1;
long[] observed = new long[binCount];
double[] expected = new double[binCount];
// Bottom bin
observed[0] = 0;
for (int i = 0; i < lower; i++) {
observed[0] += frequency.getCount(i);
}
expected[0] = poissonDistribution.cumulativeProbability(lower - 1) * sampleSize;
// Top bin
observed[binCount - 1] = 0;
for (int i = upper; i <= maxObservedValue; i++) {
observed[binCount - 1] += frequency.getCount(i);
}
expected[binCount - 1] =
(1 - poissonDistribution.cumulativeProbability(upper - 1)) * sampleSize;
// Interior bins
for (int i = 1; i < binCount - 1; i++) {
observed[i] = 0;
for (int j = binBounds.get(i - 1); j < binBounds.get(i); j++) {
observed[i] += frequency.getCount(j);
} // Expected count is (mass in [binBounds[i-1], binBounds[i])) * sampleSize
expected[i] =
(poissonDistribution.cumulativeProbability(binBounds.get(i) - 1)
- poissonDistribution.cumulativeProbability(binBounds.get(i - 1) - 1))
* sampleSize;
}
// Use chisquare test to verify that generated values are poisson(mean)-distributed
ChiSquareTest chiSquareTest = new ChiSquareTest();
// Fail if we can reject null hypothesis that distributions are the same
if (chiSquareTest.chiSquareTest(expected, observed, alpha)) {
StringBuilder msgBuffer = new StringBuilder();
DecimalFormat df = new DecimalFormat("#.##");
msgBuffer.append("Chisquare test failed for mean = ");
msgBuffer.append(mean);
msgBuffer.append(" p-value = ");
msgBuffer.append(chiSquareTest.chiSquareTest(expected, observed));
msgBuffer.append(" chisquare statistic = ");
msgBuffer.append(chiSquareTest.chiSquare(expected, observed));
msgBuffer.append(". \n");
msgBuffer.append("bin\t\texpected\tobserved\n");
for (int i = 0; i < expected.length; i++) {
msgBuffer.append("[");
msgBuffer.append(i == 0 ? 1 : binBounds.get(i - 1));
msgBuffer.append(",");
msgBuffer.append(i == binBounds.size() ? "inf" : binBounds.get(i));
msgBuffer.append(")");
msgBuffer.append("\t\t");
msgBuffer.append(df.format(expected[i]));
msgBuffer.append("\t\t");
msgBuffer.append(observed[i]);
msgBuffer.append("\n");
}
msgBuffer.append("This test can fail randomly due to sampling error with probability ");
msgBuffer.append(alpha);
msgBuffer.append(".");
Assert.fail(msgBuffer.toString());
}
}
