Related papers: On Stochastic Orders and Total Positivity
We consider the limiting distribution of the quantity $X^s/(X+Y)^r$, where $X$ and $Y$ are two independent Binomial random variables with a common success probability and a number of trials $n$ and $m$, respectively, and $r,s$ are positive…
In a generalized framework, where multi-state and inter-state linkages are allowed, we derive a sufficient condition for the stability of synchronization in a network of chaotic attractors. This condition explicitly relates the network…
``Behind every limit theorem, there is an inequality'' said Kolmogorov. We say ``for every inequality, there is an approximate inequality under approximate regularity conditions.'' Suppose $X, X'$ are independent and identically distributed…
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…
We consider probability distributions with constant rate on partially ordered sets, generalizing distributions in the usual reliability setting that have constant failure rate. In spite of the minimal algebraic structure, there is a…
We examine random variables in the power law/regularly varying class with stochastic tail exponent, the exponent $\alpha$ having its own distribution. We show the effect of stochasticity of $\alpha$ on the expectation and higher moments of…
We explore negative dependence and stochastic orderings, showing that if an integer-valued random variable $W$ satisfies a certain negative dependence assumption, then $W$ is smaller (in the convex sense) than a Poisson variable of equal…
We examine a generalization of the binomial distribution associated with a strictly increasing sequence of numbers and we prove its Poisson-like limit. Such generalizations might be found in quantum optics with imperfect detection. We…
Triangular distributions are a well-known class of distributions that are often used as an elementary example of a probability model. Maximum likelihood estimation of the mode parameter of the triangular distribution over the unit interval…
A likelihood order is defined over linear subspaces of a finite dimensional Hilbert space. It is shown that such an order that satisfies some plausible axioms can be represented by a quantum probability in two cases: pure state and uniform…
We study minimax estimation of two-dimensional totally positive distributions. Such distributions pertain to pairs of strongly positively dependent random variables and appear frequently in statistics and probability. In particular, for…
Consider a cyclically ordered collection of $r$ equinumerous agent sets with strict preferences of every agent over the agents from the next agent set. A weakly stable cyclic matching is a partition of the set of agents into disjoint union…
In this paper new families of test statistics are introduced and studied for the problem of comparing two treatments in terms of the likelihood ratio order. The considered families are based on phi-divergence measures and arise as natural…
The standard odds ratio of logistic regression is foundational but limited to individual explanatory variables. This work derives a multivariable odds ratio that applies to all the explanatory variables in all their combinations.
The stochastic comparisons of parallel and series system are worthy of study. In this paper, we present some stochastic comparisons of parallel and series systems having independent components from Gumble distribution with two parameters…
Colloquially, there are two groups, $n$ men and $n$ women, each man (woman) ranking women (men) as potential marriage partners. A complete matching is called stable if no unmatched pair prefer each other to their partners in the matching.…
Comparisons of different treatments or production processes are the goals of a significant fraction of applied research. Unsurprisingly, two-sample problems play a main role in Statistics through natural questions such as `Is the the new…
It is known that few characterization results of the logistic distribution were available before, although it is similar in shape to the normal one whose characteristic properties have been well investigated. Fortunately, in the last…
This paper conducts sensitivity analysis of random constraint and variational systems related to stochastic optimization and variational inequalities. We establish efficient conditions for well-posedness, in the sense of robust Lipschitzian…
Decisions are often based on imprecise, uncertain or vague information. Likewise, the consequences of an action are often equally unpredictable, thus putting the decision maker into a twofold jeopardy. Assuming that the effects of an action…