concentration_index: Concentration index of per-step evidence contributions

In mispitools: Missing Person Identification Tools

Concentration index of per-step evidence contributions

Description

Computes the fraction of the total absolute evidence weight carried by the single most impactful step. Ranges from 1/T (uniform contributions) to 1 (single-step dominance). Under the single-failure-mode axiomatization (Theorem T-001 in the supplementary material of Marsico & Egeland, in prep.), this is the canonical concentration measure for forensic fragility: it equals the fraction of the total weight of evidence lost under worst-case removal of a single piece of evidence.

Usage

concentration_index(weights)

Arguments

weights

Numeric vector. Per-step contributions, e.g., \log_{10}(\mathrm{LR}_k) for the two-hypothesis forensic case or per-step Kullback-Leibler divergences for the general case.

Details

The formula is

C_W(w) = \frac{\max_k |w_k|}{\sum_k |w_k|}

with absolute values taken to handle both supporting (w_k > 0) and excluding (w_k < 0) evidence symmetrically. For inclusion-fragility specifically (restricting to positive weights), use concentration_index_positive. For robustness checks, compare against herfindahl_index and shannon_concentration.

Value

Numeric scalar in [1/T, 1] where T is the length of weights. Returns 0 if all weights are zero.

References

Marsico, F. L. & Egeland, T. (in preparation). Belief dynamics during the investigative process. Slooten, K. (2021). The analogy between DNA kinship and DNA mixture evaluation. Forensic Science International: Genetics 51, 102444.

See Also

concentration_index_positive, herfindahl_index, shannon_concentration, leave_one_out.

Examples

# Balanced: all markers contribute equally
concentration_index(rep(0.7, 15))  # -> 1/15

# Concentrated: one marker dominates
concentration_index(c(5, rep(0.1, 14)))  # -> ~0.78

mispitools documentation built on Aug. 26, 2026, 1:08 a.m.