Pith Number

pith:SBUAS2QZ

pith:2026:SBUAS2QZ2WNQLMQNP7GE4EOECZ

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Modelling pairs of Poissons and binomials with negative correlation

Nils Lid Hjort

A multiplicative adjustment to independent marginal densities creates valid bivariate distributions for Poisson and binomial pairs that allow negative correlations.

arxiv:2605.17585 v1 · 2026-05-17 · stat.ME · math.ST · stat.TH

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4 Citations open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

This defines a bivariate distribution for (X,Y) with the specified marginal densities f1 and f2, with an interval of permissible values of α, both positive and negative; in particular, independence corresponds to an inner point in the adjustments parameter region.

C2weakest assumption

That bounded adjustment functions h1 and h2 exist with zero means under f1 and f2 such that the full expression remains non-negative for some negative values of α.

C3one line summary

A construction f1(x)f2(y){1 + α h1(x)h2(y)} defines bivariate distributions with specified marginals allowing negative correlation, demonstrated on Poisson plant data and binomial screening meta-analysis.

References

19 extracted · 19 resolved · 0 Pith anchors

[1] Aitchison, J. and Ho, C. (1989). The multivariate Poisson-log-normal distribution.Biometrika 76, 643–653 1989

[2] (2013).Models and Inference for Correlated Count Data.PhD Dissertation, Department of Mathematics, University of Aarhus 2013

[3] Claeskens, G. and Hjort, N.L. (2008).Model Selection and Model Averaging.Cambridge University Press, Cambridge 2008

[4] (2025).mada: Meta-Analysis of Diagnostic Accuracy,Rpackage version 0.5.12, url isCRAN.R-project.org/package=mada 2025

[5] Edwards, C.B. and Gurland, J. (1961). A class of distributions applicable to accidents.Journal of the American Statistical Association56, 503–517 1961

Receipt and verification

First computed	2026-05-20T00:04:47.310977Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9068096a19d59b05b20d7fcc4e11c4164b7e72df9cf9dc475eec35dedbc1bb51

Aliases

arxiv: 2605.17585 · arxiv_version: 2605.17585v1 · doi: 10.48550/arxiv.2605.17585 · pith_short_12: SBUAS2QZ2WNQ · pith_short_16: SBUAS2QZ2WNQLMQN · pith_short_8: SBUAS2QZ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/SBUAS2QZ2WNQLMQNP7GE4EOECZ \
  | 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: 9068096a19d59b05b20d7fcc4e11c4164b7e72df9cf9dc475eec35dedbc1bb51

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8f98945d997cca80eb4beea2f4b6b352efedce745182f4baf4cb62f4b881ed5b",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ME",
    "submitted_at": "2026-05-17T18:29:05Z",
    "title_canon_sha256": "6f0db45d4e6f89a322413e126a4f33fac360735d573ef17822349c8042e46698"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17585",
    "kind": "arxiv",
    "version": 1
  }
}