G. Letac

activity

20072022

most citedWishart distributions for decomposable graphs

113 citations · 133 across the 18 of their papers we have counts for

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13 papers · 1 filter

math.PR2022

About an extension of the Matsumoto-Yor property

Gérard Letac, Jacek Wesołowski

If $α, β > 0$ are distinct and if $A$ and $B$ are independent non-degenerate positive random variables such that $$S=\tfrac{1}{B}\,\tfrac{βA+B}{αA+B}\quad \mbox{and}\quad T=\tfrac{1}{…

math.PR2021

Duality for real and multivariate exponential families

Gérard Letac

Consider a measure $μ$ on $R^{n}$ generating a natural exponential family $F (μ)$ with variance function $V_{F (μ)} (m)$ and Laplace transform $$ \exp(\ell_μ(s))=\int_{\R^n} \exp(-\<s,…

math.PR2018

Is the Sibuya distribution a progeny?

Gérard Letac

For $0 < a < 1$ the Sibuya distribution $s_{a}$ is concentrated on the set $N^{+}$ of positive integers and is defined by the generating function $\sum_{n=1}^{\infty}s_a(n)z^n=1-(…

math.PR2017

Multivariate reciprocal inverse Gaussian distributions from the Sabot -Tarrès -Zeng integral

Gérard Letac, Jacek Wesołowski

In Sabot and Tarrès (2015), the authors have explicitly computed the integral $S T Z_{n} = \int exp (- ⟨ x, y ⟩) (det M_{x})^{- 1/2} d x$ where $M_{x}$ is a symmetric matrix of orde…

math.PR2017

Random walks in the hyperbolic plane and the question mark function

Gerard Letac, Mauro Piccioni

Consider $G = S L_{2} (Z) / {\pm I}$ acting on the complex upper half plane $H$ by $h_{M} (z) = \frac{a z + b}{cz + d},$ for $M \in G$ . Let $D = {z \in H : ∣ z ∣ \geq 1, ∣ℜ (z) ∣ \leq 1/2}$ . W…

math.PR2017

The medians for exponential families and the normal law

Gerard Letac, Lutz Mattner, Mauro Piccioni

Let $P$ a probability on the real line generating a natural exponential family $(P_{t})_{t \in R}$ . We show that $t$ is a median of $P_{t}$ for all $t$ only if $P$ is the standard Gaus…