Related papers: Convolution comparison measures
To date, testing interactions in high dimensions has been a challenging task. Existing methods often have issues with sensitivity to modeling assumptions and heavily asymptotic nominal p-values. To help alleviate these issues, we propose a…
For a probability measure $\mu$ on SL d (R), we consider the Furstenberg stationary measure on the space of flags. Under general non-degeneracy conditions, if $\mu$ is discrete and if g log g d$\mu$(g) < +$\infty$, then the measure $\nu$ is…
In this paper we give an analytic interpretation of free convolution of type B, introduced by Biane, Goodman and Nica, and provide a new formula for its computation. This formula allows us to show that free additive convolution of type B is…
In this paper, the concept of the classical $f$-divergence for a pair of measures is extended to the mixed $f$-divergence for multiple pairs of measures. The mixed $f$-divergence provides a way to measure the difference between multiple…
Let $\{f_i\}_{i=1}^N$ be a set of equi-contractive similitudes on $\mathbb{R}^1$ satisfying the finite-type condition. We study the asymptotic quantization error for self-similar measures $\mu$ associated with $\{f_i\}_{i=1}^N$ and a…
We consider the free additive convolution semigroup $\lbrace \mu^{\boxplus t}:\,t\ge 1\rbrace$ and determine the local behavior of the density of $\mu^{\boxplus t}$ at the endpoints and at any singular point of its support. We then study…
A classical theorem of Fatou asserts that the Radon-Nikodym derivative of any finite positive Borel measure, $\mu$, with respect to Lebesgue measure on the complex unit circle, is recovered as the non-tangential limits of its Poisson…
Let $\mu_{\lambda}$ be the Bernoulli convolution measure with parameter $\lambda\in(0,1)$. We study the regularity of the function %We prove that $h=h_{\phi}:\lambda\mapsto \int_{\mathbb{R}}\phi(x)\,d\mu_{\lambda}(x)$ for H\"older…
In statistics, processed data are becoming increasingly complex, and classical probability distributions are limited in their ability to model them. This is why, to better model data, extensive work has been conducted on extending classical…
Efficiency, the basic concept of multi-objective optimization is investigated for the class of pairwise comparison matrices. A weight vector is called efficient if no alternative weight vector exists such that every pairwise ratio of the…
We study the question, ``For which reals $x$ does there exist a measure $\mu$ such that $x$ is random relative to $\mu$?'' We show that for every nonrecursive $x$, there is a measure which makes $x$ random without concentrating on $x$. We…
Interpreting experimental data in high school experiments can be a difficult task for students, especially when there is large variation in the data. At the same time, calculating the standard deviation poses a challenge for students. In…
When observations are organized into groups where commonalties exist amongst them, the dependent random measures can be an ideal choice for modeling. One of the propositions of the dependent random measures is that the atoms of the…
In the paper we study characterizations of probability measures in free probability. By constancy of regressions for random variable $\V(\I-\U)\V$ given by $\V\U\V$, where $\U$ and $\V$ are free, we characterize free Poisson and free…
In a previous paper (called "Rectangular random matrices. Related covolution"), we defined, for $\lambda \in [0,1]$, the rectangular free convolution with ratio $\lambda$. Here, we investigate the related notion of infinite divisiblity,…
The conformable derivative has been promoted in numerous publications as a new fractional derivative operator. This article provides a critical reassessment of this claim. We demonstrate that the conformable derivative is not a fractional…
In any setting in which observable properties have a quantitative flavour, it is natural to compare computational objects by way of \emph{metrics} rather than equivalences or partial orders. This holds, in particular, for probabilistic…
The history based formalism known as Quantum Measure Theory (QMT) generalizes the concept of probability-measure so as to incorporate quantum interference. The resulting \textit{quantum measure} $\mu$ is defined for arbitrary events (sets…
J.C.Lagarias (2000) conjectured that if $\mu$ is a complex measure on p-dimensional Euclidean space with a uniformly discrete support and its spectrum (Fourier transform) is also a measure with a uniformly discrete support, then the support…
A phenomenon of classical quantization is discussed. This is revealed in the class of pseudoclassical gauge systems with nonlinear nilpotent constraints containing some free parameters. Variation of parameters does not change local (gauge)…