public void operateOnPartition(
PartitionDefinition definition, RowIterator inputIterator, RowEmitter outputEmitter) {
errorHandler.enterOperateOnPartition(definition, inputIterator, outputEmitter);
try {
// Collect input rows for observed and expected values
ArrayList<Double> expectedList = new ArrayList<Double>();
ArrayList<Long> observedList = new ArrayList<Long>();
while (inputIterator.advanceToNextRow()) {
errorHandler.enterOperateOnRow(inputIterator, outputEmitter);
if (inputIterator.isNullAt(observedArgumentIdx)
|| inputIterator.isNullAt(expectedArgumentIdx))
throw new IllegalArgumentException("observed and expected values cannot be null");
expectedList.add(inputIterator.getDoubleAt(expectedArgumentIdx));
observedList.add(inputIterator.getLongAt(observedArgumentIdx));
errorHandler.exitOperateOnRow();
}
double[] expected = new double[expectedList.size()];
for (int i = 0; i < expected.length; i++) expected[i] = expectedList.get(i);
long[] observed = new long[observedList.size()];
for (int i = 0; i < observed.length; i++) observed[i] = observedList.get(i);
// Run test
double pValue = chiSquareTest.chiSquareTest(expected, observed);
// Emit result
accumulator.emit(inputIterator, outputEmitter);
outputEmitter.addDouble(pValue);
outputEmitter.emitRow();
} catch (IllegalArgumentException e) {
errorHandler.catchException(e);
return; // End this partition and go to next if stopOnError is set to false (otherwise
// exception is thrown)
}
errorHandler.exitOperateOnPartition();
}
/**
* 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());
}
}