Pith. Sign in

RECORD

Regression version of the Matsumoto-Yor type characterization of the gamma and Kummer distributions

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Jacek Wesolowski

Probability · Submitted 31 Jan 2015

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We prove that constancy of regressions of U = (1 + 1/(X + Y ))=(1 + 1/X) given V = X + Y and of 1/U given V , where X and Y are indepen- dent and positive random variables, characterizes the gamma and Kummer distributions.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID1502.00140 (version 1)
Pith IDM4T3JNIE, Pith's permanent record of this paper and its review
CitationJacek Wesolowski. "Regression version of the Matsumoto-Yor type characterization of the gamma and Kummer distributions." arXiv:1502.00140 (2015). https://pith.science/paper/M4T3JNIE
Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,729 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.15 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.93 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

In this paper we study a Matsumoto-Yor type property for the gamma and Kummer inde- pendent variables discovered in Koudou and Vallois (2012). We prove that constancy of regressions of U = (1 + 1/(X + Y ))=(1 + 1/X) given V = X + Y and of 1/U given V , where X and Y are indepen- dent and positive random variables, characterizes the gamma and Kummer distributions. This result completes characterizations by independence of U and V obtained, under smoothness assumptions for densities, in Koudou and Vallois (2011, 2012). Since we work with differential equations for the Laplace transforms, no density assumptions are needed.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this paper we study a Matsumoto-Yor type property for the gamma and Kummer inde- pendent variables discovered in Koudou and Vallois (2012). background 0.57 0.40 0.05 asserted 0.83
s1 We prove that constancy of regressions of U = (1 + 1/(X + Y ))=(1 + 1/X) given V = X + Y and of 1/U given V , where X and Y are indepen- dent and positive random variables, characterizes the gamma and Kummer distributions. result 0.97 0.94 0.94 asserted 1.00
s2 This result completes characterizations by independence of U and V obtained, under smoothness assumptions for densities, in Koudou and Vallois (2011, 2012). interpretation 0.57 0.18 0.11 asserted 1.00
s3 Since we work with differential equations for the Laplace transforms, no density assumptions are needed. method 0.87 0.85 0.03 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

In this paper we study a Matsumoto-Yor type property for the gamma and Kummer inde- pendent variables discovered in Koudou and Vallois (2012). We prove that constancy of regressions of U = (1 + 1/(X + Y ))=(1 + 1/X) given V = X + Y and of 1/U given V , where X and Y are indepen- dent and positive random variables, characterizes the gamma and Kummer distributions. This result completes characterizations by independence of U and V obtained, under smoothness assumptions for densities, in Koudou and Vallois (2011, 2012). Since we work with differential equations for the Laplace transforms, no density assumptions are needed.

Human review

How Pith checks papers → · Full audit of this paper →

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.