Related papers: Quantile characterization of univariate unimodalit…
In this article we recover the distribution function (and possible density) of an arbitrary random variable that is subject to an additive measurement error. This problem is also known as deconvolution and has a long tradition in…
A general characterization for \alpha-unimodal distributions was provided by Alamatsaz (1985) who later introduced a multivariate extension of them (Alamatsaz 1993). Here, by solving the related equations, another generalization for…
We study multivariate entire functions and polynomials with non-negative coefficients. A class of {\bf Strongly Log-Concave} entire functions, generalizing {\it Minkowski} volume polynomials, is introduced: an entire function $f$ in $m$…
A real random variable admits median(s) and quantiles. These values minimize convex functions on $\mathbb R$. We show by "Convex Analysis" arguments that the function to be minimized is very natural. The relationship with some notions about…
In this paper we present a flexible bivariate distribution specified by a quantile function. The distribution contains as special cases new bivariate exponential, Pareto I, Pareto II, beta, power, log logistic and uniform distributions and…
In this paper, we propose to obtain the skewed version of a unimodal symmetric density using a skewing mechanism that is not based on a cumulative distribution function. Then we disturb the unimodality of the resulting skewed density. In…
Quantile regression relates the quantile of the response to a linear predictor. For a discrete response distributions, like the Poission, Binomial and the negative Binomial, this approach is not feasible as the quantile function is not…
We consider mesh functions which are discrete convex in the sense that their central second order directional derivatives are positive. Analogous to the case of a uniformly bounded sequence of convex functions, we prove that the uniform…
Stochastic dominance of a random variable by a convex combination of its independent copies has recently been shown to hold within the relatively narrow class of distributions with concave odds function, and later extended to broader…
In this paper, we develop a quantile functional regression modeling framework that models the distribution of a set of common repeated observations from a subject through the quantile function, which is regressed on a set of covariates to…
We study real-valued, continuous and translation invariant valuations defined on the space of quasi-concave functions of N variables. In particular, we prove a homogeneous decomposition theorem of McMullen type, and we find a representation…
As established by R T. Rockafellar, real valued convex-concave functions are generically differentiable. It this paper we shall show that for a convex-concave function defined on an open convex set $C \times D,$ there exist dense subsets…
This paper studies the convexity properties of nonsmooth extended-real-valued weakly convex functions, a class of functions that is central to modern optimization and its applications. We establish new characterizations of convexity using…
To generalize the notion of distribution function to dimension $d\geq 2$, in the recent papers it was proposed a concept of center-outward distribution function based on optimal transportation ideas, and the inferential properties of the…
This paper proposes the density and characteristic functions of a general matrix quadratic form $\mathbf{X}^{*}\mathbf{AX}$, when $\mathbf{A} = \mathbf{A}^{*}$, $\mathbf{X}$ has a matrix multivariate elliptical distribution and…
Computing explicitly the {\epsilon}-subdifferential of a proper function amounts to computing the level set of a convex function namely the conjugate minus a linear function. The resulting theoretical algorithm is applied to the the class…
For a probability P in $R^d$ its center outward distribution function $F_{\pm}$, introduced in Chernozhukov et al. (2017) and Hallin et al. (2021), is a new and successful concept of multivariate distribution function based on mass…
New criteria are shown that certain combinations of finite unimodal polynomials are unimodal. %Given unimodal polynomials with explicit expressions and dependent recursion relations, we propose an approach to determine their modes. As…
Several generalizations of the logistic distribution, and certain related models, are proposed by many authors for modeling various random phenomena such as those encountered in data engineering, pattern recognition, and reliability…
It is shown that the distribution functions of the diffusion coefficient are very similar in the standard model of quantum diffusion in a disordered metal and in a model of classical diffusion in a disordered medium: in both cases the…