actuarialmath whole-life variance squares the mean twice
The mean and second moment are correct, but an extra square produces the wrong variance. A local correction resolves 54 discrepancies across 96 independently checked synthetic cases.
GitHub: code and frozen evidence · Hugging Face · LinkedIn · Zenodo · YouTube · Maintainer correspondence (submitted)
A 46-second explanation
Original GERO diagrams and synthetic Microsoft Jenny English narration through edge-tts. Script, source ledger and production files.
Download the frozen reproducibility archive (140 KB) · Minimal source-based reproducer · Source and regression patch · Version and environment · Duplicate review
Xamit Kadirbekov / GERO Research · 14 September 2026
The discrete whole-life variance path returns an incorrect variance because it squares the first moment before passing it to a helper that squares it again. A one-line candidate correction removes that extra square. This report describes executed public source code and synthetic inputs; no insurer deployment, customer loss or production exposure was measured.
Version and scope
Repository: terence-lim/actuarialmath. Pinned main: 7d18f11ad304898f177b7922b3c53f70e4c2b4f4, project metadata 1.0.1. Current main was rechecked before publication on 14 September and was unchanged. This was a fresh source checkout imported through its src directory, not a separately tested PyPI release. Dependency versions and actual import paths are retained.
Two outcomes, an exact oracle
Take a synthetic lifetime table with death probability 0.25 in year one and certainty of death in year two conditional on surviving year one. Pay a unit benefit at the end of the year of death; the annual effective interest rate is 5%.
Let v = 1 / 1.05. The discounted benefit is v with probability 0.25 and v² with probability 0.75. Its variance is exactly 0.25 × 0.75 × (v − v²)².
from actuarialmath import LifeTable
life = LifeTable().set_table(q={40: 0.25, 41: 1}).set_interest(i=0.05)
print(life.whole_life_insurance(40, moment=life.VARIANCE))
| Quantity | Expected | Original source |
|---|---|---|
| Mean | 0.9183673469387755 | 0.9183673469387754 |
| Second moment | 0.8437842257084238 | 0.8437842257084238 |
| Variance | 0.000385641785058695 | 0.13246305434448635 |
The incorrect variance also exceeds (maximum − minimum)² / 4, the maximum possible variance for a random variable confined to that interval. This is a mathematical inconsistency under ordinary finite inputs, not a claim about real mortality experience.
Cause and candidate correction
Insurance.whole_life_insurance, line 111 computes A1 = whole_life_insurance(...)**2. The helper then calculates b**2 * max(0, A2 - A1**2). For the unit discounted benefit Y, the composition uses E[Y²] − E[Y]⁴, rather than E[Y²] − E[Y]², before applying the squared benefit scale and the nonnegative clamp.
The candidate removes only the caller's extra **2. It does not change the helper, mean, second moment or nonnegative clamp. The attached patch also adds 16 independently derived regression cases. No upstream acceptance is claimed.
Executed checks
An independent fractions.Fraction oracle enumerates 96 cases: six probabilities (0, 0.01, 0.25, 0.5, 0.9, 1), four rates (0, 0.01, 0.05, 0.2), and four benefits (0, 1, 100, 100000). The absolute tolerance, fixed before evaluating the candidate, is 32 × machine_epsilon × max(1, benefit²).
| Check | Original | Candidate |
|---|---|---|
| Incorrect variances / 96 | 54 | 0 |
| Variance range-bound violations / 96 | 54 | 0 |
| Incorrect means / 96 | 0 | 0 |
| Incorrect second moments / 96 | 0 | 0 |
| New regression tests passing / 16 | 0 on mutation replay | 16 |
Restoring the original production file reproduced all 96 original result rows exactly and failed all 16 new tests by numerical assertions. Restoring the candidate made all 16 pass again. The existing tests/test_changes.py example program also completed successfully; this is not a claim that the project has a full passing test suite. One existing SciPy deprecation warning was recorded.
Duplicate review and limits
The public upstream index contained two open/closed issue or PR records: #1 concerns UDD m-thly documentation; #2 is the prior fractional-age UDD density correction. Neither is this cause. A GitHub issues search for "actuarialmath" "whole_life_insurance" variance returned zero matches with incomplete_results=false; the guide repository and local GERO registry were also checked. The source and upstream index were refreshed before publication. This bounded search found no direct duplicate; it does not prove priority or cover private/deleted reports.
The measured scope is the discrete whole-life path via LifeTable, on a two-year finite support. Other insurance classes, real reserves, premiums and actual insurer systems were not evaluated. Existing dependency environments were reused; no fresh-machine validation is claimed. Static observations about other methods are not included as findings.
Reproduction and rights
The frozen ZIP contains the upstream source subset and MIT license, candidate patch, exact oracle, 96-case outputs, regression XML and mutation evidence. Extract it and follow its README. Preparation-stage local/unpublished labels in that immutable archive describe the earlier research state; this is the public report edition. The original ZIP is unchanged, SHA-256 678b8a2efad2a7db6c31ab416fa2dbeaa4d9406d16a5235a5bc08ed9ebf1c52b.
Independent GERO research, assisted by AI for analysis and preparation. Video diagrams are original; narration uses the synthetic Microsoft Jenny English preset through edge-tts. No affiliation with the project author or any insurer is implied.
Archive integrity
The original evidence ZIP remains byte-for-byte unchanged. Its preparation-stage draft labels are historical; this page is the public edition. The archive includes pinned source, exact oracle, test outputs and mutation replay. Follow its README for reproduction.
SHA-256: 678b8a2efad2a7db6c31ab416fa2dbeaa4d9406d16a5235a5bc08ed9ebf1c52b