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Although being a crucial question for the development of machine learning algorithms, there is still no consensus on how to compare classifiers over multiple data sets with respect to several criteria. Every comparison framework is…

Machine Learning · Statistics 2023-07-06 Christoph Jansen , Malte Nalenz , Georg Schollmeyer , Thomas Augustin

Given samples from two non-negative random variables, we propose a family of tests for the null hypothesis that one random variable stochastically dominates the other at the second order. Test statistics are obtained as functionals of the…

Statistics Theory · Mathematics 2023-10-16 Tommaso Lando , Sirio Legramanti

An approach to analyse the properties of a particle system is to compare it with different processes to understand when one of them is larger than other ones. The main technique for that is coupling, which may not be easy to construct. We…

Probability · Mathematics 2011-02-22 Davide Borrello

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…

Statistics Theory · Mathematics 2019-09-12 Tommaso Lando , Lucio Bertoli-Barsotti

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,…

Methodology · Statistics 2026-03-10 Tommaso Lando , Paulo Eduardo Oliveira

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…

Probability · Mathematics 2024-12-13 Idir Arab , Tommaso Lando , Paulo Eduardo Oliveira

The purpose of this paper is to introduce, study and analyze a new stochastic order which lies in the framework of the mean residual life and the combination convexity orders. Several preservation properties of the new order under…

Methodology · Statistics 2015-01-08 M. Kayid , S. Izadkhah , H. Alhalees

This paper considers the joint distribution of elements of a random sample and an order statistic of the same sample. \ The motivation for this work stems from the important problem in reliability analysis, to estimate the number of…

Statistics Theory · Mathematics 2019-03-04 Ismihan Bairamov

In recent years, stochastic dominance for independent and identically distributed (iid) infinite-mean random variables has received considerable attention. The literature has identified several classes of distributions of nonnegative random…

Probability · Mathematics 2026-04-28 Keyi Zeng , Zhenfeng Zou , Yuting Su , Taizhong Hu

This paper deals with testing the equality of $k$ ($k\ge 2$) distribution functions against possible stochastic ordering among them. Two classes of rank tests are proposed for this testing problem. The statistics of the tests under study…

Statistics Theory · Mathematics 2025-06-03 Nikolay I. Nikolov , Eugenia Stoimenova

In this paper, we studied the stochastic ordering behavior of series as well as parallel systems' lifetimes comprising dependent and heterogeneous components, experiencing random shocks, and exhibiting distinct dependency structures. We…

Statistics Theory · Mathematics 2025-05-29 Sarikul Islam , Nitin Gupta

Higher order risk measures are stochastic optimization problems by design, and for this reason they enjoy valuable properties in optimization under uncertainties. They nicely integrate with stochastic optimization problems, as has been…

Risk Management · Quantitative Finance 2024-02-26 Alois Pichler

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…

Statistics Theory · Mathematics 2025-06-25 Tommaso Lando , Mohammed Es-Salih Benjrada

We discuss two novel approaches to the classical two-sample problem. Our starting point are properly standardized and combined, very popular in several areas of statistics and data analysis, ordinal dominance and receiver characteristic…

Methodology · Statistics 2024-01-26 Teresa Ledwina , Adam Zagdański

Motivated by the study of the propagation of convexity by semi-groups of stochastic differential equations and convex comparison between the distributions of solutions of two such equations, we study the comparison for the convex order…

Probability · Mathematics 2024-10-11 Benjamin Jourdain , Gilles Pagès

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…

Statistics Theory · Mathematics 2017-03-14 Idir Arab , Paulo Eduardo Oliveira

We describe a new approach for managing aleatoric uncertainty in the Reinforcement Learning (RL) paradigm. Instead of selecting actions according to a single statistic, we propose a distributional method based on the second-order stochastic…

Machine Learning · Computer Science 2020-10-08 John D. Martin , Michal Lyskawinski , Xiaohu Li , Brendan Englot

In this paper, we have obtained conditions on parameters that result in dispersive ordering and star ordering among two unequal sets of random variables from Proportional hazard rate and Proportional reversed hazard rate family of…

Statistics Theory · Mathematics 2020-03-02 Madhurima Datta , Nitin Gupta

This paper proposes a nonparametric test for $m$th-degree inverse stochastic dominance which is a powerful tool for ranking distribution functions according to social welfare. We construct the test based on empirical process theory. The…

Econometrics · Economics 2023-07-18 Hongyi Jiang , Zhenting Sun , Shiyun Hu

In this paper we are interested in the joint distribution of two order statistics from overlapping samples. We give an explicit formula for the distribution of such a pair of random variables under the assumption that the parent…

Probability · Mathematics 2019-03-20 Fernando López-Blázquez , Nan-Cheng Su , Jacek Wesołowski