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pith:VATU4PQH

pith:2026:VATU4PQHAMFGF43ZSK77F6ECZN

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Formalization of the generalized Pareto principle and structural typicality of the 20/80-rule

Antti Hippel\"ainen

The generalized Pareto principle, where a fraction p of inputs produces a fraction 1-p of outputs, emerges structurally from truncated exponential and normal distributions for sample sizes between 100 and 100000, concentrating near the 20/

arxiv:2602.11131 v2 · 2026-02-11 · physics.soc-ph · math.ST · stat.TH

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Claims

C1strongest claim

datasets of size N ∈ [10^2, 10^5] from exponential and normal families concentrate p near [0.15, 0.26] and [0.20, 0.29] - values close to the canonical 0.2/0.8-rule, and strictly below the saturation k ≈ 0.865 conjectured earlier by Ghosh and Chakrabarti.

C2weakest assumption

The estimates of the truncation parameter as a function of sample size N that are combined with the closed-form expressions to produce the finite-sample predictions.

C3one line summary

A formalization of the generalized Pareto principle derives that exponential and normal distributions with 100 to 100,000 samples produce p values near 0.2, close to the 80/20 rule and below prior saturation conjectures.

References

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[1] INTRODUCTION The so-called Pareto principle or “20/80–rule” is among the most widely quoted heuristics in economics, management, and cognitive science. It states that 20% of causes result in 80% of ef

[2] fractionpof inputs yields fraction1−pof outputs

[3] EXAMPLE DISTRIBUTIONS AND EXISTENCE OF GENERALIZED PRIN- CIPLES We now examine gain density examples to illustrate how the generalized principle emerges in diverse functional forms. These cases demons

[4] In such a simple case, the decreasing rearrangement is achieved by shifting the right-hand side of the distribution to start from zero and by sendingt→t/2, so together,t→ t 2 + 1

[5] This can be thought of as the continuous version of doubling the length of every bin. Note that shifting the divergence to zero and re-normalizing is not in general equivalent to the decreasing rearra

Formal links

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Receipt and verification

First computed	2026-05-18T02:44:31.207361Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8274e3e07030a62f37992bff2f882cb4bbd1fed0bcd77e373b0235329982f82

Aliases

arxiv: 2602.11131 · arxiv_version: 2602.11131v2 · doi: 10.48550/arxiv.2602.11131 · pith_short_12: VATU4PQHAMFG · pith_short_16: VATU4PQHAMFGF43Z · pith_short_8: VATU4PQH

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/VATU4PQHAMFGF43ZSK77F6ECZN \
  | 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: a8274e3e07030a62f37992bff2f882cb4bbd1fed0bcd77e373b0235329982f82

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8df2cc30a391b4a1dbf31be64dc22b70599a0ffffbcd39bdb4f05a2993bc7f1c",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.soc-ph",
    "submitted_at": "2026-02-11T18:42:37Z",
    "title_canon_sha256": "debf97e94417c858609517d993f27a8b4bbb401c659aabc00c5c42597cc16ddb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.11131",
    "kind": "arxiv",
    "version": 2
  }
}