gistfile1.java

import java.util.*;

public class SmartpantsTst1 {

	/**
	 * @param args
	 */
	public static void main(final String[] args) {
		final Random rand = new Random();
		final int adCount = 100, impressionCount = 10000;
		final ArrayList<Double> adProbs = new ArrayList<>();
		double total = 0;
		for (int x = 0; x < adCount; x++) {
			final double p = rand.nextDouble();
			adProbs.add(p);
			total += p;
		}

		Collections.sort(adProbs);

		System.out.println("Global mean: " + total / adCount);

		final ArrayList<Integer> adImpressions = new ArrayList<>();

		for (int x = 0; x < impressionCount; x++) {
			if (rand.nextDouble() > 0.9) {
				// 50% chance that we do genuine random selection
				adImpressions.add(rand.nextInt(adCount));
			} else {
				final int pos = adCount - (int) Math.round((Math.pow(rand.nextDouble() * Math.sqrt(adCount), 2))) - 1;
				if (pos < 0 || pos >= adCount) {
					continue;
				}
				adImpressions.add(pos);
			}
		}

		final int[] occurances = new int[adCount];
		double rawSum = 0;
		for (final int x : adImpressions) {
			occurances[x]++;
			rawSum += adProbs.get(x);
		}

		System.out.println("Raw mean:  " + rawSum / adImpressions.size());

		double correctedTotal = 0, correctedSum = 0;

		for (final int x : adImpressions) {
			final double bias = 1.0 / occurances[x];
			correctedTotal += bias;
			correctedSum += adProbs.get(x) * bias;
		}

		System.out.println("Corrected mean: " + (correctedSum / correctedTotal));
	}

}