{
  "annotation_id": "bc9461c8-91db-4019-92ee-8a053f21fb0c",
  "date_created": "2026-03-02T18:00:42.215000Z",
  "date_modified": "2026-03-02T18:00:42.215000Z",
  "file_hash": "e4fabd6235bfe83950e68373a96119cf80112d61acf8d9b99a822857dc50e164",
  "private": false,
  "record": {
    "abstract": "Fisher information is a measure of the best precision with which a parameter\ncan be estimated from statistical data. It can also be defined for a continuous\nrandom variable without reference to any parameters, in which case it has a\nphysically compelling interpretation of representing the highest precision with\nwhich the first cumulant of the random variable, i.e., its mean, can be\nestimated from its statistical realizations. We construct a complete hierarchy\nof information measures that determine the best precision with which all of the\ncumulants of a random variable -- and thus its complete probability\ndistribution -- can be estimated from its statistical realizations. Several\nproperties of these information measures and their generating functions are\ndiscussed.",
    "arxiv_id": "physics/0212035",
    "authors": [
      "S. Prasad",
      "N. C. Menicucci"
    ],
    "categories": [
      "physics.data-an"
    ],
    "doi": "10.1109/TIT.2004.825034",
    "journal_ref": "IEEE Trans. Inf. Theory 50, 638-642 (2004)",
    "title": "Fisher Information With Respect to Cumulants",
    "url": "https://arxiv.org/abs/physics/0212035"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "fc0725f1-d064-44cb-9fd2-3f88deb9b456",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}