Pith Number

pith:I2IYMHMY

pith:2026:I2IYMHMYFLRD63LP6XAYRWKVLN

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An approximate formula for the entropy of the negative binomial distribution

S\'andor L\"ok\"os

The Shannon entropy of the negative binomial distribution admits a simple approximate formula that deviates by at most about 20 percent from the exact value for extreme parameter values.

arxiv:2605.11147 v3 · 2026-05-11 · hep-ph

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\pithnumber{I2IYMHMYFLRD63LP6XAYRWKVLN}

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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

we will investigate one of these and give an approximate formula for the entropy that is valid up to ∼20% deviation from the exact value for extreme values of the NBD parameters.

C2weakest assumption

The approximation relies on the behavior of one series or integral representation of the NBD entropy and assumes that the stated 20% deviation bound holds across the relevant extreme parameter regimes without additional validation details.

C3one line summary

An approximate formula for the entropy of the negative binomial distribution is given, accurate to within 20% for extreme parameter values.

Receipt and verification

First computed	2026-05-20T00:04:35.923679Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4691861d982ae23f6d6ff5c188d9555b4c5fb5ed483e19d1b69b9513f5499d78

Aliases

arxiv: 2605.11147 · arxiv_version: 2605.11147v3 · doi: 10.48550/arxiv.2605.11147 · pith_short_12: I2IYMHMYFLRD · pith_short_16: I2IYMHMYFLRD63LP · pith_short_8: I2IYMHMY

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/I2IYMHMYFLRD63LP6XAYRWKVLN \
  | 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: 4691861d982ae23f6d6ff5c188d9555b4c5fb5ed483e19d1b69b9513f5499d78

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "10d795378f54580060989cb5a9243f7fa6a54a6c4d0d08402bca61d1c5984472",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2026-05-11T18:53:41Z",
    "title_canon_sha256": "15d05363c9503a8c181906e8211c20c4af2ae6e422e32e19d0c7d9042c9f3572"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.11147",
    "kind": "arxiv",
    "version": 3
  }
}