Pith Number

pith:LDCABCY4

pith:2026:LDCABCY4NMWXCMXMA7HMZNZLEM

not attested not anchored not stored refs resolved

Median Radial Function: A Robust, Covariance-Free Framework and Applications

Elsayed Elamir

A median radial depth function measures centrality in multivariate data without covariance or moment assumptions.

arxiv:2605.13439 v1 · 2026-05-13 · stat.ME

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LDCABCY4NMWXCMXMA7HMZNZLEM}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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

The depth function is robust to outliers and independent of covariance structure; it does not depend on moment assumptions and naturally adapts to skewness, multimodality, and heavy-tailed distributions.

C2weakest assumption

That median distances from an appropriately chosen center can serve as the basis for a statistically valid and useful depth function without additional moment or distributional assumptions.

C3one line summary

A new median radial function defines a covariance-free, outlier-robust depth measure for multivariate data that adapts to skewness and multimodality.

References

2 extracted · 2 resolved · 0 Pith anchors

[1] Boente, G., & Salibián-Barrera, M. (2021). Robust functional principal components for sparse longitudinal data. METRON, 79(2), 159–188. https://doi.org/10.1007/s40300- 020-00193-3 Boyd, S., & Vandenbe 2021 · doi:10.1007/s40300-

[2] On the Generalised Distance in Statistics 2019 · doi:10.1007/s42519-021-00236-6

Receipt and verification

First computed	2026-05-18T02:44:47.058056Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

58c4008b1c6b2d7132ec07ceccb72b2321af7d21ca7ce8be824b6121d18c7c39

Aliases

arxiv: 2605.13439 · arxiv_version: 2605.13439v1 · doi: 10.48550/arxiv.2605.13439 · pith_short_12: LDCABCY4NMWX · pith_short_16: LDCABCY4NMWXCMXM · pith_short_8: LDCABCY4

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/LDCABCY4NMWXCMXMA7HMZNZLEM \
  | 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: 58c4008b1c6b2d7132ec07ceccb72b2321af7d21ca7ce8be824b6121d18c7c39

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "42616435cafa11499464360e691a17f99644d09f98a5e5504f2b64fc3145d5ca",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ME",
    "submitted_at": "2026-05-13T12:36:00Z",
    "title_canon_sha256": "84aa00c7670f2f618e66f3c3216f58e64801f38e56113750f558c3a7a3c3caed"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13439",
    "kind": "arxiv",
    "version": 1
  }
}