// Generate sample values
int sampleSize = 1000; // Number of deviates to generate
int minExpectedCount = 7; // Minimum size of expected bin count
long maxObservedValue = 0;
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 PoissonDistributionImpl(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 = 1;
boolean widthSufficient = false;
double lowerBinMass = 0;
double upperBinMass = 0;
while (!widthSufficient) {
lowerBinMass = poissonDistribution.cumulativeProbability(lower, lower + binWidth - 1);
upperBinMass = poissonDistribution.cumulativeProbability(upper - binWidth + 1, upper);
widthSufficient = Math.min(lowerBinMass, upperBinMass) * sampleSize >= minExpectedCount;
binWidth++;
}
/*
* 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(bound);
binBounds.add(upper);
// 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], binBounds[i+1])) * sampleSize
expected[i] = (poissonDistribution.cumulativeProbability(binBounds.get(i) - 1) -
poissonDistribution.cumulativeProbability(binBounds.get(i - 1) -1)) * sampleSize;
}