Claim size ($X_j\ge 0$)

The monetary amount of an individual insurance claim. Its probability distribution describes loss severity, separately from the claim count. In an independent random sum of independent claims, severity mean $\mu$ and expected count combine to give aggregate mean $\mathbb{E}N\mu$.

Claims claims inflation changes the monetary size of a claim over calendar time. With a fixed annual rate $r$, a time-zero size $c_0$ becomes the displayed end-of-year amount. Historical claim amounts must be converted to a common price year before their empirical monetary averages are combined. When the per-claim amounts are known, dividing total amount by the year's per-claim amount recovers the claim count.