Fit per-link ED intensity factors

Estimate per-development-link incremental loss intensities \(g_k = \mathbb{E}[\Delta L_k / C^P_k]\) from a "Triangle" and return an "IntensityFit" object that bundles the link-level WLS-estimated intensities along with their standard errors and diagnostic statistics.

This is the factor-level diagnostic for the exposure-driven (ED) workflow, parallel to fit_ata() for the multiplicative (chain ladder) side. Both operate at the factor level without producing a full projection. For full ED projection (cumulative loss / premium / ratio), use fit_ed() which accepts either a Triangle or an IntensityFit (skipping a rebuild of the link table when factors are already computed).

Usage

fit_intensity(
  x,
  loss = "loss",
  exposure = "premium",
  alpha = 1,
  na_method = c("locf", "zero", "none"),
  sigma_method = c("locf", "min_last2", "loglinear", "mack", "none"),
  recent = NULL,
  regime = NULL,
  ...
)

Arguments

x: A Triangle object.
loss: A single cumulative metric used as the link numerator. Default "loss".
exposure: A single cumulative metric used as the exposure base (denominator anchor). Default "premium".
alpha: WLS weight exponent. Default 1.
na_method: NA fill method for the selected intensity series used downstream by fit_ed(). One of "locf" (default – carries the last observed intensity forward, appropriate for long-term health where ageing keeps \(g_k\) elevated rather than decaying to 0), "zero" (sets late-dev NAs to 0; suits short-tail lines where claims fully settle), or "none".
sigma_method: Method used to extrapolate sigma for links where it cannot be estimated. One of "locf" (default), "min_last2", "loglinear", "mack", or "none". "mack" applies the Mack (1993, Appendix B) tail estimator to the last unestimated link only, falling back to LOCF for any earlier ones with a warning. "none" performs no extrapolation; sigma stays NA and downstream variance terms drop those links via finite-value guards. Passed to .extrapolate_sigma_ata().
recent: Optional positive integer. When supplied, restricts estimation to rows within the last recent calendar diagonals (calendar-diagonal wedge filter; see .apply_recent_filter()).
regime: Optional regime specification for cohort cutoff. Accepts: NULL (default – no filter), a "Regime" object (from detect_regime()), the string "auto" (internal detect_regime(tri, loss = "ratio") call), or a function function(tri) -> Regime. Resolved internally via .resolve_regime(). When supplied, cohorts strictly before the change are dropped before estimation.
...: Passed to summary.Link() (e.g. digits).

Value

A list of class "IntensityFit" with components:

call: The matched call.
data: The (possibly filtered) Link object used for estimation.
groups, cohort, dev, loss, premium: Variable name relays from the input Triangle.
link: Alias of data for parallelism with fit_ata().
factor: The EDSummary returned by summary.Link() – one row per link with WLS-estimated g, g_se, rse, sigma, plus descriptive statistics.
selected: data.table of selected intensities per link (g_sel, sigma, sigma2, sigma_extrapolated). LOCF NA-fill is applied when na_method = "locf"; sigma extrapolation is applied per sigma_method.
alpha, na_method, sigma_method, recent, regime: Call metadata. regime is the resolved "Regime" object (or NULL) returned by .resolve_regime().

ED has no maturity concept

Unlike ATA factors, where CV / RSE drive a detect_maturity() threshold, ED intensities behave differently – as \(g_k \to 0\) in late development the CV / RSE blow up by construction, not by instability. fit_intensity() therefore deliberately omits a maturity parameter, and detect_maturity() rejects IntensityFit input with an informative error.

Examples

if (FALSE) { # \dontrun{
tri <- as_triangle(
  df,
  groups   = "coverage",
  cohort   = "uy_m",
  calendar = "cy_m",
  loss     = "incr_loss",
  premium  = "incr_premium"
)
intensity_fit <- fit_intensity(tri, loss = "loss", exposure = "premium")
summary(intensity_fit)
} # }

Usage

Arguments

Value

ED has no maturity concept

See also

Examples