{
  "annotation_id": "aeac001a-ae8b-4af5-a12c-869a1be6b63a",
  "date_created": "2026-03-02T18:01:07.972000Z",
  "date_modified": "2026-03-02T18:01:07.972000Z",
  "file_hash": "883ba7d66b9d6dbc372f474325bb2d1b38ee218a0b3e107b5f70c6332d96e03e",
  "private": false,
  "record": {
    "abstract": "We discuss a general method to construct correlated binomial distributions by\nimposing several consistent relations on the joint probability function. We\nobtain self-consistency relations for the conditional correlations and\nconditional probabilities. The beta-binomial distribution is derived by a\nstrong symmetric assumption on the conditional correlations. Our derivation\nclarifies the \u0027correlation\u0027 structure of the beta-binomial distribution. It is\nalso possible to study the correlation structures of other probability\ndistributions of exchangeable (homogeneous) correlated Bernoulli random\nvariables. We study some distribution functions and discuss their behaviors in\nterms of their correlation structures.",
    "arxiv_id": "physics/0605189",
    "authors": [
      "M. Hisakado",
      "K. Kitsukawa",
      "S. Mori"
    ],
    "categories": [
      "physics.data-an"
    ],
    "doi": "10.1088/0305-4470/39/50/005",
    "journal_ref": "J.Phys.A:Math.Gen.39(2006)15365-15378",
    "title": "Correlated Binomial Models and Correlation Structures",
    "url": "https://arxiv.org/abs/physics/0605189"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a02046cd-fe3b-4ddf-856b-6cce5a36f10d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}