Une caractérisation des familles exponentielles de Riesz

Lajmi, S.

doi:10.1016/s0764-4442(97)80138-3

Cited by 2 publications

(4 citation statements)

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“…For the proof of Theorem , we need to recall some preliminary results. The first result is proved in Lajmi ; it gives the first and the second derivatives of the cumulant generating function

k_{R_{s}} (θ) = \ln (L_{R_{s}} (θ))

of a Riesz measure R s .…”

Section: Proofsmentioning

confidence: 97%

“…The second class corresponds to s in

normal Ξ ∖ \prod_{i = 1}^{r}] (i - 1) \frac{d}{2}, + \infty [

. In this case, the Riesz measure R s is concentrated on the boundary ∂ Ω of Ω; it has a complicated form that is explicitly described in Lajmi .…”

Section: Introductionmentioning

confidence: 99%

“…In this case, the Riesz measure R s is concentrated on the boundary @ of ; it has a complicated form that is explicitly described in Lajmi [11]. For s D .s 1 , , s r / in " and in , we define the Riesz probability distribution R r .s, / by…”

Section: Introductionmentioning

confidence: 99%

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Some new properties of the Riesz probability distribution

Hassairi

Lajmi

Zine

2017

Math Methods in App Sciences

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The Riesz probability distribution on any symmetric cone and, in particular, on the cone of positive definite symmetric matrices represents an important generalization of the Wishart and of the matrix gamma distributions containing them as particular examples. The present paper is a continuation of the investigation of the properties of this probability distribution. We first establish a property of invariance of this probability distributions by a subgroup of the orthogonal group. We then show that the Pierce components of a Riesz random variable are independent, and we determine their probability distributions. Some moments and some useful expectations related to the Riesz probability distribution are also calculated. Copyright © 2017 John Wiley & Sons, Ltd.

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“…For the proof of Theorem , we need to recall some preliminary results. The first result is proved in Lajmi ; it gives the first and the second derivatives of the cumulant generating function

k_{R_{s}} (θ) = \ln (L_{R_{s}} (θ))

of a Riesz measure R s .…”

Section: Proofsmentioning

confidence: 97%

“…The second class corresponds to s in

normal Ξ ∖ \prod_{i = 1}^{r}] (i - 1) \frac{d}{2}, + \infty [

. In this case, the Riesz measure R s is concentrated on the boundary ∂ Ω of Ω; it has a complicated form that is explicitly described in Lajmi .…”

Section: Introductionmentioning

confidence: 99%

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Some new properties of the Riesz probability distribution

Hassairi

Lajmi

Zine

2017

Math Methods in App Sciences

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“…Proof of Theorem 3.4. Differentiating (6) with respect to x gives a ′ 1 (x) = t * g ′ (tx) − t * g ′ (t(e − x)).…”

mentioning

confidence: 99%

A characterization of the Riesz distribution

Hassairi,

Lajmi,

Zine

2007

Preprint

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Bobecka and Wesolowski (2002) have shown that, in the Olkin and Rubin characterization of the Wishart distribution (See Casalis and Letac (1996)), when we use the division algorithm defined by the quadratic representation and replace the property of invariance by the existence of twice differentiable densities, we still have a characterization of the Wishart distribution. In the present work, we show that, when we use the division algorithm defined by the Cholesky decomposition, we get a characterization of the Riesz distribution.

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Une caractérisation des familles exponentielles de Riesz

Cited by 2 publications

References 4 publications

Some new properties of the Riesz probability distribution

Some new properties of the Riesz probability distribution

A characterization of the Riesz distribution

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