{
  "abstract": "We introduce this class of multivariate Kappa-Gaussian distributions by maximizing a type of Kaniadakis $κ$ entropy subject to certain first- and second-moment constraints. This differs slightly from the approach of Rényi and Tsallis, because the $κ$-entropy arises from a relativity-consistent deformation of the exponential and logarithmic functions and yields a family of distributions whose tails follow a power law, a family that actually reverts to the standard Gaussian distribution as $κ\\to 0$. We then create a $k$-nearest-neighbor (NN) estimator for $κ$-entropy and describe it using the difference between two NN functionals involving sums of powers. Next, we establish $L^2$-consistency and asymptotic normality, using the well-known subadditive Euclidean functional and moment expansion framework for NN entropy estimators. Furthermore, using a scaling identity for the $κ$-exponential, we derive a closed-form formula for the entropy of the $κ$-Gaussian distribution itself. From this, we determine the exact threshold value $κ< 2/(m+2)$ at which the distribution preserves finite variance; this is analogous to the ``degrees of freedom $>2$'' condition in the Student's-$t$ distribution. With these components, we construct a non-parametric goodness-of-fit test and then verify it through simulations. Finally, we mention the Sharma--Mittal entropy, which combines the Rényi and Tsallis entropies as a natural direction for future work.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06873",
  "author_total": 2,
  "authors": [
    {
      "name": "Mehmet Siddik Cadirci"
    },
    {
      "name": "Konstantinos Zografos"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3mkx8wp7ew9y9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06873",
  "fulltext_url": null,
  "id": "3mkx8wp7ew9y9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06873",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "3109|Statistical Mechanics and Entropy"
    ]
  ],
  "openalex": "W7220969235",
  "pdf_url": "https://arxiv.org/pdf/2610.06873",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3mkx8wp7ew9y9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.06873",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06873"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Entropy-Based Goodness-of-Fit Tests for Generalized $κ$ -Gaussian Distributions",
  "title_text": "Entropy-Based Goodness-of-Fit Tests for Generalized κ -Gaussian Distributions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:32Z",
  "url": "https://research.draconitic.com/paper/3mkx8wp7ew9y9",
  "venue": "arXiv",
  "versions": []
}