Related papers: The normal distribution is $\boxplus$-infinitely d…
The Tukey-$\lambda$ distribution has interesting properties including (i) for some parameters values it has finite support, and for others infinite support, and (ii) it can mimic several other distributions such that parameter estimation…
We show that all negative powers B_{a,b}^-{s} of the Beta distribution are infinitely divisible. The case b<1 follows by complete monotonicity, the case b > 1, s > 1 by hyperbolically complete monotonicity and the case b > 1, s < 1 by a…
We discuss in detail the asymptotic distribution of sample expectiles. First, we show uniform consistency under the assumption of a finite mean. In case of a finite second moment, we show that for expectiles other then the mean, only the…
A new family of integer-valued Cauchy-type distributions is introduced, the {\it Cauchy-Cacoullos family}. The characteristic function is evaluated, showing some interesting distributional properties, similar to the ordinary (continuous)…
The Weibull distribution can be obtained using a power transformation from the standard exponential distribution. In this article, we will consider a symmetrized power transformation of a random variable with the standard normal…
If there is a topologically locally constant family of smooth algebraic varieties together with an admissible normal function on the total space, then the latter is constant on any fiber if this holds on some fiber. Combined with spreading…
Let $d \geq 3$ be a natural number. We show that for all finite, non-empty sets $A \subseteq \mathbb{R}^d$ that are not contained in a translate of a hyperplane, we have \[ |A-A| \geq (2d-2)|A| - O_d(|A|^{1- \delta}),\] where $\delta >0$ is…
The extended de Finetti theorem characterizes exchangeable infinite random sequences as conditionally i.i.d. and shows that the apparently weaker distributional symmetry of spreadability is equivalent to exchangeability. Our main result is…
The theory of distributions provides generalized solutions for problems which do not have a classical solution. However, there are problems which do not have solutions, not even in the space of distributions. As model problem you may think…
Computing the embedding distribution of a given graph is a fundamental question in topological graph theory. In this article, we extend our viewpoint to a sequence of graphs and consider their asymptotic embedding distributions, which are…
Under usual locality assumptions, we classify all non-integrable distributions with simple infinite-dimensional Lie superalgebra of symmetries over $\mathbb{C}$: we single out 15 series (containing 2 analogs of contact series and one family…
This paper describes the quality of convergence to an infinitely divisible law relative to free multiplicative convolution. We show that convergence in distribution for products of identically distributed and infinitesimal free random…
The paper studies Dirichlet forms on the classical Wiener space and the Wiener space over non-compact complete Riemannian manifolds. The diffusion operator is almost everywhere an unbounded operator on the Cameron--Martin space. In…
This paper completes the foundations of neatly integrable normal distribution theory on manifolds with boundary. Normal distributions are those which contain vectors transverse to the boundary along its entirety. The theory is observed to…
We obtain a formula for the density of the free convolution of an arbitrary probability measure on the unit circle of $\mathbb{C}$ with the free multiplicative analogues of the normal distribution on the unit circle. This description relies…
We study Boolean stable laws, $\mathbf{b}_{\alpha,\rho}$, with stability index $\alpha$ and asymmetry parameter $\rho$. We show that the classical scale mixture of $\mathbf{b}_{\alpha,\rho}$ coincides with a free mixture and also a monotone…
We investigate some regularity properties of a class of doubly nonlinear anisotropic evolution equations whose model case is \begin{align*} \partial_t \big(|u|^{\alpha -1}u \big) - \sum^N_{i=1} \partial_i \big( |\partial_i u|^{p_i - 2}…
In order to better fit real-world datasets, studying asymmetric distribution is of great interest. In this work, we derive several mathematical properties of a general class of asymmetric distributions with positive support which shows up…
A new class of distributional transformations is introduced, characterized by equations relating function weighted expectations of test functions on a given distribution to expectations of the transformed distribution on the test function's…
It is shown that the universal theory of the free pseudocomplemented distributive lattice is decidable and a recursive axiomatization is presented. This contrasts with the case of the full elementary theory of the finitely generated free…