mack_stochastic
Estimates distribution-free standard errors and coefficients of variation for chain-ladder reserve projections, providing uncertainty measures per accident year and in total.
Instructions
Mack (1993) stochastic chain-ladder error estimation. Returns distribution-free standard errors and coefficients of variation per accident row plus the totals — the canonical sensitivity check for a deterministic chain-ladder result.
Use this when the user asks about uncertainty, reserve risk, or
confidence intervals. Pair it with compute_chain_ladder (use the
same selected_factors for consistency).
Args:
triangle: As in compute_chain_ladder.
selected_factors: The factors used for the point-estimate
projection. Length = n_dev - 1.
excluded: Outlier exclusions to honour, same shape as in
compute_chain_ladder.
Returns:
- sigma2: list[float] — σ̂_j² per development period; backfilled
via Mack's tail rule when only one observation is available
- se_per_row: list[float] — standard error of each ultimate
- cv_per_row: list[float] — coefficient of variation (SE /
Ultimate) per accident row
- se_total: float — SE of the sum of all ultimates (includes
cross-row covariance per Mack eq. 5.15)
- cv_total: float — CV of the total ultimate
Input Schema
| Name | Required | Description | Default |
|---|---|---|---|
| triangle | Yes | ||
| selected_factors | Yes | ||
| excluded | No |
Output Schema
| Name | Required | Description | Default |
|---|---|---|---|
No arguments | |||