Characterization of the simple cubic multivariate exponential families

AbstractThe Letac–Mora class of real cubic natural exponential families has been characterized by a property of 2-orthogonality of an associated sequence of polynomials (see [G. Letac, M. Mora, Natural real exponential families with cubic variance functions, Ann. Statist. 18 (1990) 1–37; A. Hassairi, M. Zarai, Characterization of the cubic exponential families by orthogonality of polynomials, Ann. Probab. 32 (2004) 2463–2476]). The present paper introduces a notion of transorthogonality for a sequence of polynomial on Rd to extend the characterization to the multivariate version of the Letac–Mora class of real natural exponential families

Cosmic ray studies with a streamer chamber

A streamer chamber system has been developed to study the multiple scattering of cosmic rays at sea level. The thesis described new electronic circuits for the control of the system, and a new method for applying high voltage pulses of short duration. Multiple scattering studies have been conducted with one inch slabs of lead and mercury. When 138 MeV muons were identified by their decay electron, excellent agreement was obtained with the Cooper and Rainwater theory. Without this identification anomalous results were obtained. During the course of the research, an interesting new effect has been observed---the appearance of rings on the Lichtenberg figures associated with the discharge in the chamber.<p

Phenotypic Progression of Stargardt Disease in a Large Consanguineous Tunisian Family Harboring New ABCA4 Mutations.

To assess the progression of Stargardt (STGD) disease over nine years in two branches of a large consanguineous Tunisian family. Initially, different phenotypes were observed with clinical intra- and interfamilial variations. At presentation, four different retinal phenotypes were observed. In phenotype 1, bull's eye maculopathy and slight alteration of photopic responses in full-field electroretinography were observed in the youngest child. In phenotype 2, macular atrophy and yellow white were observed in two brothers. In phenotype 3, diffuse macular, peripapillary, and peripheral RPE atrophy and hyperfluorescent dots were observed in two sisters. In phenotype 4, Stargardt disease-fundus flavimaculatus phenotype was observed in two cousins with later age of onset. After a progression of 9 years, all seven patients displayed the same phenotype 3 with advanced stage STGD and diffuse atrophy. WES and MLPA identified two &lt;i&gt;ABCA4&lt;/i&gt; mutations M1: c.[(?_4635)_(5714+?)dup; (?_6148)_(6479_+?) del] and M2: c.[2041C&gt;T], p.[R681 &lt;sup&gt;∗&lt;/sup&gt; ]. In one branch, the three affected patients had M1/M1 causal mutations and in the other branch the two affected patients had M1/M2 causal mutations. After 9-year follow-up, all patients showed the same phenotypic evolution, confirming the progressive nature of the disease. Genetic variations in the two branches made no difference to similar end-stage disease

On the projections of the Dirichlet probability distribution on symmetric cones

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Extension of the variance function of a steep exponential family

AbstractLet F={P(m,F);m∈MF} be a multidimensional steep natural exponential family parameterized by its domain of the means MF and let VF(m) be its variance function. This paper studies the boundary behaviour of VF. Necessary and sufficient conditions on a point m of ∂MF are given so that VF admits a continuous extension VF(m) to the point m . It is also shown that the existence of VF(m) implies the existence of a limit distribution P(m,F) concentrated on an exposed face of MF containing m. The relation between VF(m) and P(m,F) is established and some illustrating examples are given

Characterizations of the beta distribution on symmetric matrices

This paper extends to the beta-Wishart distribution on symmetric matrices, two characterizations of the beta distributions on , due to Seshadri and Wesolowski and based on some properties of constancy regression.Wishart distribution Beta distribution Orthogonal group Spherical Fourier transform Regression