Earlier researchers have studied some aspects of the classes of distribution functions with decreasing ?-percentile residual life (DPRL(?)), 0 ? 1. The purpose of this paper is to note some further properties of these classes, and to initiate a theory of nonparametric statistical estimation of...

In this paper we study a family of stochastic orders of random variables defined via the comparison of their percentile residual life functions. Some interpretations of these stochastic orders are given, and various properties of them are derived. The relationships to other stochastic orders are...

Let X1:n≤X2:n⋯≤Xn:n be the order statistics from some sample, and let Y[1:n],Y[2:n],…,Y[n:n] be the corresponding concomitants. One purpose of this paper is to obtain results that stochastically compare, in various senses, the random vector (Xr:n,Y[r:n]) to the random vector...

In this paper we study convolution residuals, that is, if <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$X_1,X_2,\ldots ,X_n$$</EquationSource> </InlineEquation> are independent random variables, we study the distributions, and the properties, of the sums <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$\sum _{i=1}^lX_i-t$$</EquationSource> </InlineEquation> given that <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$\sum _{i=1}^kX_it$$</EquationSource> </InlineEquation>, where <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$t\in \mathbb R $$</EquationSource> </InlineEquation>, and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$$1\le k\le l\le n$$</EquationSource> </InlineEquation>....</equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation>

We settle an open conjecture regarding the newsvendor game. We prove that its core is always nonempty for all possible joint distributions of the random demands. We give sufficient conditions under which the core is a singleton, or at a core allocation every newsvendor shares a nonnegative cost

The authors study new notions of positive dependence that are associated to multivariate stochastic orders of positive dependence introduced recently by Colangelo et al. [J. Multivar. Anal., to appear]. In particular, they discuss the relationship of these new notions to other existing concepts...

In this note we compare bivariate additive models with respect to their Pearson correlation coefficients, Kendall’s τ concordance coefficients, and Blomqvist β medial correlation coefficients. The conditions that enable the comparisons involve variability stochastic orders such as the...

In this paper we establish multivariate hazard rate, multivariate reverse hazard rate, and multivariate likelihood ratio stochastic orderings among multivariate random mapping (mixture) distributions. The new results streamline and simplify the proofs of some partial results that have recently...

The literature on "weighted k-out-of-n" systems is briefly reviewed. The concept may result in systems with quite a broad array of possible structures and thus seems more aptly described by the phrase "systems with weighted components (SWCs)". It is observed that a system with weighted...