Pith Number

pith:KVDHTITJ

pith:2026:KVDHTITJ5YY24GRHAF57D4XHWV

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Quantifying Dependence Between Random Vectors: A New Index with Applications

Chuancun Yin

A new index for random vectors equals zero exactly when they are sub-independent and takes all values in [0,1].

arxiv:2605.16970 v1 · 2026-05-16 · math.ST · stat.TH

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Claims

C1strongest claim

The proposed index takes values in [0,1] and equals zero if and only if the random vectors are sub-independent.

C2weakest assumption

That the characteristic-function construction yields an index that is exactly zero under sub-independence and positive otherwise, as asserted without detailed derivation in the abstract.

C3one line summary

Introduces a dependence index for random vectors in [0,1] that vanishes if and only if the vectors are sub-independent, constructed via characteristic functions with empirical and asymptotic results.

References

25 extracted · 25 resolved · 0 Pith anchors

[1] Statistical Theory of Reliability and Life Testing: Probability Models 1975

[2] Convexity and measures of statistical association 2025

[3] B¨ ottcher, B., Keller-Ressel, M., Schilling, R. L., 2019. Distance multi- variance: new dependence measures for random vectors. Ann. Statist. 47 (5), 2757-2789 2019

[4] Estimation of varying coefficient models with measurement error 2022

[5] Durairajan, T. M., 1979. A classroom note on sub-independence. Gu- jarat Statist. Rev. VI: 17-18 1979

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-20T00:03:33.643572Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

554679a269ee31ae1a27017bf1f2e7b54a1cd89128c59161872581c895df3b9f

Aliases

arxiv: 2605.16970 · arxiv_version: 2605.16970v1 · doi: 10.48550/arxiv.2605.16970 · pith_short_12: KVDHTITJ5YY2 · pith_short_16: KVDHTITJ5YY24GRH · pith_short_8: KVDHTITJ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/KVDHTITJ5YY24GRHAF57D4XHWV \
  | 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: 554679a269ee31ae1a27017bf1f2e7b54a1cd89128c59161872581c895df3b9f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c37663a533e241536657ec6a247add1eaf141b5729680fd9420b2114a9e88418",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2026-05-16T12:43:35Z",
    "title_canon_sha256": "87b193459e08016704970e0f26c1722ec9c26ea6272256df5840e443dfaa0d51"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16970",
    "kind": "arxiv",
    "version": 1
  }
}