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pith:5Y47J5LR

pith:2026:5Y47J5LR4U7DOM4VHETQ222EKF

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The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions

Heather L. Sutcliffe, Robert E. Gaunt

Exact series and integral formulas are derived for the densities of sums and differences of independent non-central gamma random variables.

arxiv:2605.15386 v1 · 2026-05-14 · math.PR

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Claims

C1strongest claim

Exact formulas are derived for the probability density functions of the sum and difference of two independent non-central gamma distributed random variables, with both series and integral representations of the density presented.

C2weakest assumption

The two random variables are independent and each follows a non-central gamma distribution (with the series and integral representations converging for the given parameter values).

C3one line summary

Exact distributions and asymptotic expansions derived for sums and differences of independent non-central gamma random variables, including closed-form coefficients for the product of correlated normals.

References

50 extracted · 50 resolved · 1 Pith anchors

[1] Bateman, H., Erd´ elyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G.Higher Transcendental Func- tions Volume 1.McGraw-Hill, 1953 1953

[2] On the efficient calculation of a linear combination of chi-square random variables with an appli- cation in counting string vacua.J 2013

[3] and L´ opez-Bl´ azquez, F 2005

[4] and L´ opez-Bl´ azquez, F 2005

[5] Right-tail asymptotics for products of independent normal random variables 2026 · arXiv:2603.08570

Formal links

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Receipt and verification

First computed	2026-05-20T00:00:55.821181Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee39f4f571e53e37339539270d6b4451525209c9afb47a95376ed3200219cff3

Aliases

arxiv: 2605.15386 · arxiv_version: 2605.15386v1 · doi: 10.48550/arxiv.2605.15386 · pith_short_12: 5Y47J5LR4U7D · pith_short_16: 5Y47J5LR4U7DOM4V · pith_short_8: 5Y47J5LR

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/5Y47J5LR4U7DOM4VHETQ222EKF \
  | 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: ee39f4f571e53e37339539270d6b4451525209c9afb47a95376ed3200219cff3

Canonical record JSON

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    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-14T20:15:45Z",
    "title_canon_sha256": "92de822745dbaea0d8864aef3eb376655f945df181d0706b41c09ce1bd20247d"
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