Count summaries depend on the number J of units. The population weight functionals answer different questions.
| Quantity | Question | Report |
|---|---|---|
| E(K_J), Var(K_J) | How many patterns among these J units, and how certain? | Expected count and uncertainty interval |
| P(K_J = k) | What is the chance of exactly k patterns? | Mode and central interval |
| P(W_SB > .5), P(W_SB > .9) | Could a randomly selected unit belong to a majority-mass or near-universal-mass population cluster? | Probability for the size-biased weight |
| P(W_max > t) | Could the largest population cluster exceed mass t? | Bounds or exact probability |
| rho = sum(w_h^2) | Will two randomly selected units share a pattern? | Probability of same-cluster membership |