Related papers: Convex transform order of Beta distributions with …
Recently, expectile-based measures of skewness akin to well-known quantile-based skewness measures have been introduced, and it has been shown that these measures possess quite promising properties (Eberl and Klar, 2021, 2020). However, it…
Convex combinations of i.i.d. random variables without a finite mean can behave in a strikingly different way from the finite-mean case: as the weight vector becomes more balanced, the resulting combination may become stochastically larger,…
Consider a sequence of polynomials of bounded degree evaluated in independent Gaussian, Gamma or Beta random variables. We show that, if this sequence converges in law to a nonconstant distribution, then (i) the limit distribution is…
In this work, we consider the sample complexity required for testing the monotonicity of distributions over partial orders. A distribution $p$ over a poset is monotone if, for any pair of domain elements $x$ and $y$ such that $x \preceq y$,…
The distributional properties of the translation flow on the unit square have been considered in different fields of mathematics, including algebraic geometry and discrepancy theory. One method to quantify equidistribution is to compare the…
This paper studies the log-convexity of the extended beta functions. As a consequence, Tur\'an-type inequalities are established.The monotonicity, log-convexity, log-concavity of extended hypergeometric functions are deduced by using the…
The (strong) Bruhat order for permutations provides a partial ordering defined as follows: two permutations are comparable if one can be obtained from the other by a sequence of adjacent transpositions that each increase the number of…
We give a method for proactively identifying small, plausible shifts in distribution which lead to large differences in model performance. These shifts are defined via parametric changes in the causal mechanisms of observed variables, where…
Some special functions are particularly relevant in applied probability and statistics. For example, the incomplete beta function is the cumulative central beta distribution. In this paper, we consider the inversion of the central…
We study an optimal weak transport cost related to the notion of convex order between probability measures. On the real line, we show that this weak transport cost is reached for a coupling that does not depend on the underlying cost…
The Birnbaum-Saunders distribution is a flexible and useful model which has been used in several fields. In this paper, a new bimodal version of this distribution based on the alpha-skew-normal distribution is established. We discuss some…
The polygonal distributions are a class of distributions that can be defined via the mixture of triangular distributions over the unit interval. The class includes the uniform and trapezoidal distributions, and is an alternative to the beta…
We explore negative dependence and stochastic orderings, showing that if an integer-valued random variable $W$ satisfies a certain negative dependence assumption, then $W$ is smaller (in the convex sense) than a Poisson variable of equal…
A class of probability distributions is characterized via equalities in law between two order statistics shifted by independent exponential variables. An explicit formula for the quintile function of the identified family of distributions…
This note contains sufficient conditions for the probability density function of an arbitrary continuous univariate distribution, supported on $(0,\infty),$ such that the corresponding Mills ratio to be reciprocally convex (concave). To…
Given two independent samples of non-negative random variables with unknown distribution functions $F$ and $G$, respectively, we introduce and discuss two tests for the hypothesis that $F$ is less than or equal to $G$ in increasing convex…
Most work on supervised learning research has focused on marginal predictions. In decision problems, joint predictive distributions are essential for good performance. Previous work has developed methods for assessing low-order predictive…
This paper concerns a method of testing equality of distribution of random convex compact sets and the way how to use the test to distinguish between two realisations of general random sets. The family of metrics on the space of…
This article reviews recent advances in convex optimization algorithms for Big Data, which aim to reduce the computational, storage, and communications bottlenecks. We provide an overview of this emerging field, describe contemporary…
We introduce the beta generalized exponential distribution that includes the beta exponential and generalized exponential distributions as special cases. We provide a comprehensive mathematical treatment of this distribution. We derive the…