Internal helper computing \(\mathrm{Var}(\hat{g}_k) = \sigma^2_k / W_k\) where \(W_k = \sum_i (C^P_{i,k})^{2 - \alpha}\). This is the Buehlmann-Straub (1970) volume-weighted variance applied to the ED intensity \(g_k = \sum_i \Delta L_{i,k} / \sum_i P_{i,k-1}\).
Paradigm pairing: the package keeps two natural analytical variance
helpers, one per paradigm-target pair: .mack_f_var() (CL / Mack 1993
applied to f-factor) and .ed_g_var() (ED / Buehlmann-Straub 1970
applied to g-intensity). The cross-paradigm pairs (.mack_g_var,
.bs_f_var) are algebraically derivable via \(g_k = f_k - 1\)
(and therefore \(\sigma^2_g = \sigma^2_f\)), so are intentionally
not provided as separate functions to avoid suggesting paradigm
mismatch is encouraged in user code.
Conceptually a factor-level helper (operates on per-link $link
and $selected slots), parallel to .mack_f_var(ata_fit: ATAFit).
Accepts either "IntensityFit" (the factor-level diagnostic for
ED, sibling of "ATAFit") or "EDFit" (projection-level,
which exposes the same factor-level slots as a superset). The
"IntensityFit" path is the conceptually clean entry point for
factor-level callers; "EDFit" is accepted for projection-level
callers that already hold the fit object.
Used by fit_ed() when method = "mack" and by fit_ratio() for the
ED component.
References
Buehlmann, H. and Straub, E. (1970). Glaubwuerdigkeit fuer Schadensaetze (Credibility for Loss Ratios). Bulletin of the Swiss Association of Actuaries, 70, 111-133.
Mack, T. (1993). Distribution-free calculation of the standard error of chain ladder reserve estimates. ASTIN Bulletin, 23(2), 213-225.