Pith Number

pith:QBDYUQWW

pith:2026:QBDYUQWWCJV4ZGSYN5ZRLTF2PN

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A Note on the Folding Test of Unimodality: limitation and improved alternative

Anne M. Ruiz, Aurore Archimbaud, Colombe Becquart, Zaineb Smida

The folding test of unimodality misclassifies certain multimodal mixtures as unimodal, but a double-folding version corrects the error.

arxiv:2605.13326 v1 · 2026-05-13 · stat.ME

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Claims

C1strongest claim

the folding-based criterion can systematically fail, misclassifying clearly multimodal distributions as unimodal. We fully characterize these failures for Dirac mixtures and extend the analysis to Gaussian mixtures. We then introduce a double-folding procedure that captures complementary information, leading to a new test, the Double Folding Test of Unimodality. It resolves the FTU failures and improves multimodality detection power in simulations.

C2weakest assumption

That applying the folding operation twice captures complementary information about modality without introducing new biases or reducing detection power in non-mixture or other distribution settings.

C3one line summary

The Double Folding Test of Unimodality resolves systematic failures of the original FTU on Dirac and Gaussian mixtures and enhances multimodality detection.

References

24 extracted · 24 resolved · 0 Pith anchors

[1] The annals of Statistics , pages= 1985

[2] Are your data gathered? , abstract =

[3] New statistical methods for data mining, contributions to anomaly detection and unimodality testing , copyright = 2019

[4] arXiv preprint arXiv:2311.16614 , author =

[5] Journal of the Royal Statistical Society Series B: Statistical Methodology , author = 1981

Receipt and verification

First computed	2026-05-18T02:44:48.616490Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

80478a42d6126bcc9a586f7315ccba7b7e825b999e1c2ea355339648c5b5e3ae

Aliases

arxiv: 2605.13326 · arxiv_version: 2605.13326v1 · doi: 10.48550/arxiv.2605.13326 · pith_short_12: QBDYUQWWCJV4 · pith_short_16: QBDYUQWWCJV4ZGSY · pith_short_8: QBDYUQWW

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/QBDYUQWWCJV4ZGSYN5ZRLTF2PN \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 80478a42d6126bcc9a586f7315ccba7b7e825b999e1c2ea355339648c5b5e3ae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "370993d3ab16aa30fbad6235be5219e44fccec73cca7568b815f82b43a90edc4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ME",
    "submitted_at": "2026-05-13T10:40:11Z",
    "title_canon_sha256": "272bf61f58f668f1dc5d11c667a13a577ea5447a6ccab46681c3704624c2a075"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13326",
    "kind": "arxiv",
    "version": 1
  }
}