Related papers: Statistical convergence of order $\alpha$ in proba…
The sequence of $\alpha$-trimmings of empirical probabilities is shown to converge, in the Painlev\'{e}--Kuratowski sense, on the class of probability measures endowed with the weak topology, to the $\alpha$-trimming of the population…
In this paper we obtain some possibilistic variants of the probabilistic laws of large numbers, different from those obtained by other authors, but very natural extensions of the corresponding ones in probability theory. Our results are…
The need to condition distributional properties such as expectation, variance, and entropy arises in algorithmic fairness, model simplification, robustness and many other areas. At face value however, distributional properties are not…
In this paper, we use a new partial order, called the f-majorization order. The new order includes as special cases the majorization , the reciprocal majorization and the p-larger orders. We provide a comprehensive account of the…
In many empirical studies of a large two-sided matching market (such as in a college admissions problem), the researcher performs statistical inference under the assumption that they observe a random sample from a large matching market. In…
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…
The univariate extreme value theory deals with the convergence in type of powers of elements of sequences of cumulative distribution functions on the real line when the power index gets infinite. In terms of convergence of random variables,…
Let $\alpha_n(\cdot)=P\bigl(X_{n+1}\in\cdot\mid X_1,\ldots,X_n\bigr)$ be the predictive distributions of a sequence $(X_1,X_2,\ldots)$ of $p$-dimensional random vectors. Suppose $$\alpha_n= \mathcal{N} _p (M_n,Q_n)$$ where…
An equivalent condition for the product of elements of an independent random sample on a compact algebraic group converging in distribution to some random variable as the sample size increases is obtained. Namely, a limit distribution…
Conventional statistics begins with a model, and assigns a likelihood of obtaining any particular set of data. The opposite approach, beginning with the data and assigning a likelihood to any particular model, is explored here for the case…
Here I discuss ideas that makes a synthesis of topology and probability theory. The idea is the following: given a set $X$, assign a number $p(A)\in [0,1]$ for any subset $A$ of $X$. We can interpret $p(A)$ as the probability of openness of…
In this note, we study a class of random subsets of positive integers induced by Bernoulli random variables. We obtain sufficient conditions such that the random set is almost surely lacunary, does not have bounded gaps and contains…
In comparative studies, such as in causal inference and clinical trials, balancing important covariates is often one of the most important concerns for both efficient and credible comparison. However, chance imbalance still exists in many…
The probability density quantile (pdQ) carries essential information regarding shape and tail behavior of a location-scale family. Convergence of repeated applications of the pdQ mapping to the uniform distribution is investigated and new…
A random set is a generalisation of a random variable, i.e. a set-valued random variable. The random set theory allows a unification of other uncertainty descriptions such as interval variable, mass belief function in Dempster-Shafer theory…
For a bivariate random vector (X,Y), symmetry conditions are presented that yield stochastic orderings among |X|, |Y|, |max(X,Y)|, and | min(X, Y)|. Partial extensions of these results for multivariate random vectors (X1,...,Xn) are also…
Many axiomatic definitions of entropy, such as the R\'enyi entropy, of a random variable are closely related to the $\ell_{\alpha}$-norm of its probability distribution. This study considers probability distributions on finite sets, and…
We study the relationship between the growth rate of an integer sequence and harmonic and functional properties of the corresponding sequence of characters. In particular we show that every polynomial sequence contains a set that is…
A new class of general exponential ranking models is introduced which we label angle-based models for ranking data. A consensus score vector is assumed, which assigns scores to a set of items, where the scores reflect a consensus view of…
Statistical convergence was introduced in connection with problems of series summation. The main idea of the statistical convergence of a sequence l is that the majority of elements from l converge and we do not care what is going on with…