Related papers: Integrated quantile functions: properties and appl…
We derive the exact probability density function of the product of $N$ independent variance-gamma random variables with zero location parameter. We then apply this formula to derive formulas for the cumulative distribution function and…
The family of skew-symmetric distributions is a wide set of probability density functions obtained by combining in a suitable form a few components which are selectable quite freely provided some simple requirements are satisfied. Intense…
The classical concept of Fenchel conjugation is tailored to extended real-valued functions defined on linear spaces. In this paper we generalize this concept to functions defined on arbitrary sets that do not necessarily bear any structure…
An integral in the sense of principal value of a singular function or of product of singular functions can appear itself as a singular function in some range of values of integration parameters. In this case, if necessary subsequently to…
The use of charge balance functions in heavy-ion collision studies was initially proposed as a probe of delayed hadronization and two-stage quark production in these collisions. It later emerged that general balance functions can also serve…
Let $X$ and $Y$ be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the product $XY$ is derived. Some basic distributional properties are also derived, including…
In this paper, we study integral functionals defined on spaces of functions with values on general (non-separable) Banach spaces. We introduce a new class of integrands and multifunctions for which we obtain measurable selection results.…
We study the problem of modeling univariate distributions via their quantile functions. We introduce a flexible family of distributions whose quantile function is a linear combination of basis quantiles. Because the model is linear in its…
The purpose of the present paper is to give unified expressions to the characteristic functions of all elliptical and related distributions. Those distributions including the multivariate elliptical symmetric distributions and some…
In this paper we examine quantile-stratified samples from a known univariate probability distribution, with stratification occurring over a partition of the quantile regions in the distribution. We examine some general properties of this…
We show that there is a way to unify distribution functions that describe simultaneously a signal in space and (spatial) frequency. Probably the most known of them is the Wigner distribution function. Here we show how to unify functions of…
The quantum theory can be formulated in the language of positive functionals on Weyl or Clifford algebra ($L$-functionals). It is shown that this language gives simple understanding of diagrams of Keldysh formalism (that coincide in our…
A fundamental problem in statistics and learning theory is to test properties of distributions. We show that quantum computers can solve such problems with significant speed-ups. In particular, we give fast quantum algorithms for testing…
We illustrate the potential applications in machine learning of the Christoffel function, or more precisely, its empirical counterpart associated with a counting measure uniformly supported on a finite set of points. Firstly, we provide a…
Geometric quantiles are popular location functionals to build rank-based statistical procedures in multivariate settings. They are obtained through the minimization of a non-smooth convex objective function. As a result, the singularity of…
We study the moments and the distribution of the discrete Choquet integral when regarded as a real function of a random sample drawn from a continuous distribution. Since the discrete Choquet integral includes weighted arithmetic means,…
Integrable probability has emerged as an active area of research at the interface of probability/mathematical physics/statistical mechanics on the one hand, and representation theory/integrable systems on the other. Informally, integrable…
We provide theoretical error bounds for the accurate numerical computation of the quantile function given the characteristic function of a continuous random variable. We show theoretically and empirically that the numerical error of the…
In this review article we present regularity properties of generalized functions which are useful in the analysis of non-linear problems. It is shown that Schwartz distributions embedded into our new spaces of generalized functions, with…
Application of the exact statistical inference frequently leads to a non-standard probability distributions of the considered estimators or test statistics. The exact distributions of many estimators and test statistics can be specified by…