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Read the outcome mass
In the original model, loss 10 has probability 25%. The cumulative distribution rises from 70% below 10 to 95% at 10. That positive mass is an atom, not a continuous range of nearby loss amounts.
Keep the jump in the record
| Quantity | Probability |
|---|---|
| Loss strictly below 10 | 70% |
| Loss equal to 10 | 25% |
| Loss at or below 10 | 95% |
Include only the selected portion when needed
At 90% confidence, the exact worst-tail average uses 5% probability from loss 10 plus all 5% at loss 50. The economic loss remains 10 for the included boundary portion; only its inclusion weight changes.
Combine identical loss values consistently
Several mutually exclusive scenario records may produce the same loss. Adding their probabilities leaves the distribution unchanged. Splitting or merging those records should not change the quantile or expected-shortfall result.