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In this paper, we study stochastic ordering results between two finite mixtures with single and multiple outliers, assuming subpopulations follow general exponentiated location-scale distributions. For single-outlier mixtures, several…
Comparing concentration properties of uniform sampling with and without replacement has a long history which can be traced back to the pioneer work of Hoeffding (1963). The goal of this short note is to extend this comparison to the case of…
Dispersive order is a type of variability order for comparing the variability in probability distributions. Star order compares the skewness of probability distributions. This work considers dispersive and star orders of extreme order…
The aim of the present work is to provide a supplement to the authors' paper (2018). It is shown that our results on the approximation of distributions of sums of independent summands by the accompanying compound Poisson laws and the…
Strassen's theorem asserts that for given marginal probabilities $\mu,\nu$ there exists a martingale starting in $\mu$ and terminating in $\nu$ if and only if $\mu,\nu$ are in convex order. From a financial perspective, it guarantees the…
We study odd numbers through a straightforward indexing. We focus in particular on odd prime and composite numbers and their distribution. With a counting argument, we calculate the limit of two sums and compare their convergence rate.
Predictive distributions need to be aggregated when probabilistic forecasts are merged, or when expert opinions expressed in terms of probability distributions are fused. We take a prediction space approach that applies to discrete, mixed…
In this article, we discuss a bivariate distribution whose conditionals are univariate binomial distributions and the marginals are not binomial that exhibits negative correlation. Some useful structural properties of this distribution…
Posterior predictive p-values are a common approach to Bayesian model-checking. This article analyses their frequency behaviour, that is, their distribution when the parameters and the data are drawn from the prior and the model…
In multiple importance sampling we combine samples from a finite list of proposal distributions. When those proposal distributions are used to create control variates, it is possible (Owen and Zhou, 2000) to bound the ratio of the resulting…
The problem of convergence in law of normed sums of exchangeable random variables is examined. First, the problem is studied w.r.t. arrays of exchangeable random variables, and the special role played by mixtures of products of stable laws…
In this paper, we introduce a convergence notion for ordered selections. Our convergence notion is based on subpermutation densities and convergences of the marginal distributions. A particular case of this convergence is the well-known…
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…
Coupling probability measures lies at the core of many problems in statistics and machine learning, from domain adaptation to transfer learning and causal inference. Yet, even when restricted to deterministic transports, such couplings are…
In distributionally robust optimization the probability distribution of the uncertain problem parameters is itself uncertain, and a fictitious adversary, e.g., nature, chooses the worst distribution from within a known ambiguity set. A…
A number of writers have supposed that for the full specification of belief, higher order probabilities are required. Some have even supposed that there may be an unending sequence of higher order probabilities of probabilities of…
We consider positively supported Borel measures for which all moments exist. On the set of compactly supported measures in this class a partial order is defined via eventual dominance of the moment sequences. Special classes are identified…
Positive dependencies have been compared in the literature under rather strong assumptions such as equality of conditional distributions, exchangeability, or stationarity. We establish supermodular ordering results for distributions that…
The study of sums of possibly associated Bernoulli random variables has been hampered by an asymmetry between positive correlation and negative correlation. The Conway-Maxwell Binomial (COMB) distribution and its multivariate extension, the…
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…