Pith Number

pith:L6YNKTIO

pith:2026:L6YNKTIOT4YFVK5LYROUHYOTXV

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Parameter estimation for kappa distributions using the EM algorithm in the superstatistical framework

Leonardo Herrera-Fuenzalida, Sergio Davis

Modeling inverse temperature as a gamma-distributed latent variable recovers the exponential family structure for kappa distributions and yields a closed-form EM algorithm for parameter estimation.

arxiv:2605.05428 v2 · 2026-05-06 · stat.ME · cond-mat.stat-mech · physics.plasm-ph

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\pithnumber{L6YNKTIOT4YFVK5LYROUHYOTXV}

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Claims

C1strongest claim

This enables an implementation of the expectation-maximization (EM) algorithm in analytically closed form, with E-step and M-step derived from sufficient statistics.

C2weakest assumption

The inverse temperature β is introduced as a gamma-distributed latent variable that recovers the exponential family structure in the complete-data likelihood.

C3one line summary

Data augmentation with a gamma latent inverse temperature recovers the exponential family for kappa distributions, allowing a closed-form EM algorithm for maximum likelihood estimation in the superstatistics framework.

Receipt and verification

First computed	2026-05-22T01:03:19.815118Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5fb0d54d0e9f305aababc45d43e1d3bd412663f57c449382d4ec3e9eaa7441c4

Aliases

arxiv: 2605.05428 · arxiv_version: 2605.05428v2 · doi: 10.48550/arxiv.2605.05428 · pith_short_12: L6YNKTIOT4YF · pith_short_16: L6YNKTIOT4YFVK5L · pith_short_8: L6YNKTIO

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/L6YNKTIOT4YFVK5LYROUHYOTXV \
  | 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: 5fb0d54d0e9f305aababc45d43e1d3bd412663f57c449382d4ec3e9eaa7441c4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "57d0233aec481fa586b106698a6b9ed3b5ce7ae18f0e54d91ffc673c2b3e1f30",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "physics.plasm-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ME",
    "submitted_at": "2026-05-06T20:37:35Z",
    "title_canon_sha256": "32f06db7b5fe4aab15ee86121452206e558f746d3d33fb2388705cc41e8a5245"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.05428",
    "kind": "arxiv",
    "version": 2
  }
}