Related papers: Demi-linear Analysis III -- Demi-distributions wit…
We prove that the classical normal distribution is infinitely divisible with respect to the free additive convolution. We study the Voiculescu transform first by giving a survey of its combinatorial implications and then analytically,…
The existence of a formal particular solution (family of solutions) of oscillating type under certain conditions has been proved for the quasi-linear ordinary differential equations system. The asymptotic nature of this solution (the family…
Generalizing classic results for a family of measures in the torus, for a family $(\mu_t)_{t\geq 0}$ of measures defined on a nilmanifold $X$, we study conditions under which the family equidistributes, meaning conditions under which the…
The statistics of meander and related problems are studied as particular realizations of compact polymer chain foldings. This paper presents a general discussion of these topics, with a particular emphasis on three points: (i) the use of a…
In this paper three new characterizing theorems of exponential distribution are presented. They are based on equidistribution of some functions of order statistics. All of them include the median of sample of size three.
In the context of survival analysis, Marshall and Olkin (1997) introduced families of distributions by adding a scalar parameter to a given survival function, parameterized or not. In that paper, we generalize their approach. We show how it…
The paper gives a wide range, uniform, local approximation of symmetric binomial distribution. The result clearly shows how one has to modify the the classical de Moivre--Laplace normal approximation in order to give an estimate at the tail…
In two recent articles we have examined a generalization of the binomial distribution associated with a sequence of positive numbers, involving asymmetric expressions of probabilities that break the symmetry {\it win-loss}. We present in…
A three-dimensional integrable generalization of the St\"ackel systems is proposed. The classification of such systems is obtained which results in two families. The first one is the direct sum of the two-dimensional case which is…
In the present paper, we endow a family of axiomatic extensions of semi De Morgan logic with proper multi-type display calculi which are sound, complete, conservative, and enjoy cut elimination and subformula property. Our proposal builds…
Finite mixtures of regression models offer a flexible framework for investigating heterogeneity in data with functional dependencies. These models can be conveniently used for unsupervised learning on data with clear regression…
This paper is on developing stochastic analysis simultaneously under a general family of probability measures that are not dominated by a single probability measure. The interest in this question originates from the probabilistic…
Sine-skewed circular distributions are identifiable and have easily-computable trigonometric moments and a simple random number generation algorithm, whereas they are known to have relatively low levels of asymmetry. This study proposes a…
It is known that for every $s\in]1,2[$ there is a copula whose support is a self-similar fractal set with Hausdorff -- and box-counting -- dimension $s$. In this paper we provide similar results for (proper) quasi-copulas, in both the…
Dickson's commutative semifields are an important class of finite division algebras. We generalise Dickson's construction of commutative division algebras by doubling both finite field extensions and central simple algebras and not…
The paper deals with a generalisation of uniform distribution. The analogues of Weyl's criterion are derived.
This note aims at providing a guide towards the use of mild distributions, or more generally the concept of Banach Gelfand Triples in the context of Fourier Analysis, both in the classical and the application oriented sense.
In this paper, a new class of distributions, called Odds xgamma-G (OXG-G) family of distribu- tions is proposed for modeling lifetime data. A comprehensive account of the mathematical proper- ties of the new class including estimation issue…
A new family of Gaussian-type SIGMA basis sets, termed reduced SIGMA basis sets, is introduced and preliminarily tested. Sharing the same composition as Dunning basis sets, they enhance performance by reducing linear dependencies in large…
We consider the classical problem of discrete distribution estimation using i.i.d. samples in a novel scenario where additional side information is available on the distribution. In large alphabet datasets such as text corpora, such side…