Related papers: Transform orders and stochastic monotonicity of st…
Stochastic orders are binary relations defined on probability distributions which capture intuitive notions like being larger or being more variable. This paper introduces stochastic ordering of instantaneous SNRs of fading channels as a…
Stochastic monotonicity is a well known partial order relation between probability measures defined on the same partially ordered set. Strassen Theorem establishes equivalence between stochastic monotonicity and the existence of a coupling…
We study a generalized family of stochastic orders, semiparametrized by a distortion function H, namely H-distorted stochastic dominance, which may determine a continuum of dominance relations from the first- to the second-order stochastic…
The focus of this article is on entropy and Markov processes. We study the properties of functionals which are invariant with respect to monotonic transformations and analyze two invariant "additivity" properties: (i) existence of a…
We introduce a comprehensive method for establishing stochastic orders among order statistics in the i.i.d. case. This approach relies on the assumption that the underlying distribution is linked to a reference distribution through a…
Spaces with locally varying scale of measurement, like multidimensional structures with differently scaled dimensions, are pretty common in statistics and machine learning. Nevertheless, it is still understood as an open question how to…
In this paper we introduce a biparametric family of transformations which can be seen as an extension of the so-called up and down transformations. This new class of transformations allows to us to introduce new informational functionals,…
Stochastic ordering of distributions of random variables may be defined by the relative convexity of the tail functions. This has been extended to higher order stochastic orderings, by iteratively reassigning tail-weights. The actual…
This paper generalizes the notion of stochastic order to a relation between probability measures over arbitrary measurable spaces. This generalization is motivated by the observation that for the stochastic ordering of two stationary Markov…
The Transformed-Transformer family of distributions are the resulting family of distributions as transformed from a random variable $T$ through another transformer random variable $X$ using a weight function $\omega$ of the cumulative…
The preservation of stochastic orders by distortion functions has become a topic of increasing interest in the reliability analysis of coherent systems. The reason of this interest is that the reliability function of a coherent system with…
This manuscript investigates the stochastic comparisons of the second-order statistics from dependent and heterogeneous general semi-parametric family of distributions observations. Some sufficient conditions on the usual stochastic order…
Modelling stochastic systems has many important applications. Normal form coordinate transforms are a powerful way to untangle interesting long term macroscale dynamics from detailed microscale dynamics. We explore such coordinate…
This paper aims to study a new stochastic order based upon discrete Laplace transforms. By this order, in a setup where the sample size is random, having discrete delta and nabla distributions, we obtain some ordering results involving…
Let $\mu$ be a probability measure on $\mathbb{R}$. We give conditions on the Fourier transform of its density for functionals of the form $H(a)=\int_{\mathbb{R}^n}h(\langle a,x\rangle)\mu^n(dx)$ to be Schur monotone. As applications, we…
The convex transform order is one way to make precise comparison between the skewness of probability distributions on the real line. We establish a simple and complete characterisation of when one Beta distribution is smaller than another…
Ordinal measures provide a valuable collection of tools for analyzing correlated data series. However, using these methods to understand the information interchange in networks of dynamical systems, and uncover the interplay between…
A new thresholding method, based on L-statistics and called order thresholding, is proposed as a technique for improving the power when testing against high-dimensional alternatives. The new method allows great flexibility in the choice of…
Consider a pair of cumulative distribution functions $F$ and $G$, where $F$ is unknown and $G$ is a known reference distribution. Given a sample from $F$, we propose tests to detect the convexity or the concavity of $G^{-1}\circ F$ versus…
We simplify the proof of some widely used theoretical theorems, extending their applicability, while correcting some erroneous results. We also generalize key results and present new results that contribute to the development of the theory.…