Severity Distribution Fitter
Fit lognormal, gamma, and Pareto severity curves to claim data via MLE with goodness-of-fit diagnostics.
Mean
1,808
Std. dev.
2,370
CV
131.1%
Mean excess @ threshold
25,233
Probability density function
Quantiles
| Percentile | Value |
|---|---|
| 50.0% | 1,097 |
| 90.0% | 3,950 |
| 99.0% | 11,230 |
| 99.5% | 14,412 |
Limited expected value (LEV)
| Limit | E[X ∧ L] |
|---|---|
| 25,000 | 1,800 |
| 50,000 | 1,807 |
| 100,000 | 1,808 |
| 250,000 | 1,808 |
| 500,000 | 1,808 |
| 1,000,000 | 1,808 |
| 2,000,000 | 1,808 |
| 5,000,000 | 1,808 |
Increased limits factors
| Limit | ILF |
|---|---|
| 25,000 | 0.996 |
| 50,000 | 0.999 |
| 100,000 | 1.000 |
| 250,000 | 1.000 |
| 500,000 | 1.000 |
| 1,000,000 | 1.000 |
| 2,000,000 | 1.000 |
| 5,000,000 | 1.000 |
Layer expected loss & mean excess
Layer expected loss
0
Mean excess loss (e(d))
25,233
Assumptions & limitations
- The fitted curve represents the ground-up severity distribution net of any deductible or truncation in the underlying data.
- Lognormal fit uses MLE on log-losses; gamma fit uses method of moments; Pareto MLE assumes a known threshold near the sample minimum.
- LEV, ILF, and layer figures are theoretical (parametric) values — no risk load, ALAE treatment, or trend has been applied.