Pith Number

pith:HJ7IZWOI

pith:2026:HJ7IZWOIYGFKVIKKHO2GJGCXOE

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Testing the Structural Properties of Marked Point Processes Using Local Inhomogeneous Mark-Weighted K-Functions

Giada Adelfio, Matthias Eckardt, Nicoletta D'Angelo

Chi-squared tests based on local inhomogeneous mark-weighted K-functions detect global and local deviations from independence or homogeneity in marked point patterns.

arxiv:2605.13187 v1 · 2026-05-13 · stat.ME · stat.AP

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Claims

C1strongest claim

The methodology proves to be effective in identifying both global and localised departures from the null hypotheses, even in scenarios with subtle mark structures or small sample sizes.

C2weakest assumption

The local inhomogeneous extension of the mark-weighted K-function accurately captures mark-location interactions without bias from density estimation or bandwidth choices in the local windows.

C3one line summary

Chi-squared tests using local inhomogeneous mark-weighted K-functions can identify global and local deviations from null hypotheses in marked point patterns, even with subtle structures or small samples.

References

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[1] Biometrical Journal: Journal of Mathematical Methods in Biosciences , volume= 1998

[2] Testing separability in spatial-temporal marked point processes , author=. Biometrics , pages=. 2004 , publisher= 2004

[3] Journal of Computational and Graphical Statistics , volume = 2026

[4] Journal of Agricultural, Biological and Environmental Statistics , year= · doi:10.1007/s13253-024-00605-1

[5] Journal of Agricultural, Biological and Environmental Statistics , year= · doi:10.1007/s13253-024-00613-1

Receipt and verification

First computed	2026-05-18T03:08:56.212245Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3a7e8cd9c8c18aaaa14a3bb46498577112a65aabe54e9b43ec461592ef45a4a7

Aliases

arxiv: 2605.13187 · arxiv_version: 2605.13187v1 · doi: 10.48550/arxiv.2605.13187 · pith_short_12: HJ7IZWOIYGFK · pith_short_16: HJ7IZWOIYGFKVIKK · pith_short_8: HJ7IZWOI

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/HJ7IZWOIYGFKVIKKHO2GJGCXOE \
  | 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: 3a7e8cd9c8c18aaaa14a3bb46498577112a65aabe54e9b43ec461592ef45a4a7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4d7e748715bee96add1788e155743fb75a724d73236fe5895ed2efa1627ffd1f",
    "cross_cats_sorted": [
      "stat.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ME",
    "submitted_at": "2026-05-13T08:43:38Z",
    "title_canon_sha256": "ae24057d213367beba3f9ec3bdbae44ad138cca88b6d75676a7c91b7d023c2af"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13187",
    "kind": "arxiv",
    "version": 1
  }
}