Related papers: Order statistics from exchangeable random variable…

Given a sequence $(X_n)$ of symmetrical random variables taking values in a Hilbert space, an interesting open problem is to determine the conditions under which the series $\sum_{n=1}^\infty X_n$ is almost surely convergent. For…

This work investigates the intersection property of conditional independence. It states that for random variables $A,B,C$ and $X$ we have that $X$ independent of $A$ given $B,C$ and $X$ independent of $B$ given $A,C$ implies $X$ independent…

A characterization of the exponential distribution based on equidistribution conditions for maxima of random samples with consecutive sizes n-1 and n for an arbitrary and fixed n>2 is proved. This solves an open problem stated recently in…

Given disjoint subsets $T_1,\ldots,T_m$ of "not too large" primes up to $x$, we establish that for a random integer $n$ drawn from $[1,x]$, the $m$-dimensional vector enumerating the number of prime factors of $n$ from $T_1,\ldots,T_m$…

For fixed $t = 2$ or $3$, we investigate the statistical properties of $\{Y_t(n)\}$, the sequence of random variables corresponding to the number of hook lengths divisible by $t$ among the partitions of $n$. We characterize the support of…

Let $X_{1}=(W_{1},Y_{1}),\ldots,X_{n}=(W_{n},Y_{n})$ be $n$ pairs of independent random variables. We assume that, for each $i\in\{1,\ldots,n\}$, the conditional distribution of $Y_{i}$ given $W_{i}$ belongs to a one-parameter exponential…

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…

This study presents new estimates for fractional derivatives without singular kernels defined by some specific functions. Based on obtained inequalities, we give a useful method to establish the global stability of steady states for…

Let $M_n^{(k)}$ denote the $k$th largest maximum of a sample $(X_1,X_2,...,X_n)$ from parent $X$ with continuous distribution. Assume there exist normalizing constants $a_n>0$, $b_n\in \mathbb{R}$ and a nondegenerate distribution $G$ such…

This paper focuses on a data-rich environment where the data set has a very large cross-sectional dimension, is likely to exhibit local dependence, and yet is hard to determine the dependence ordering. Such a situation arises, for example,…

Given a sequence \xi_1, \xi_2,... of X-valued, exchangeable random elements, let q(\xi^(n)) and p_m(\xi^(n)) stand for posterior and predictive distribution, respectively, given \xi^(n) = (\xi_1,..., \xi_n). We provide an upper bound for…

In this paper, we have discussed the usual stochastic ordering relations between two systems. Each system consists of n mutually independent components. The components follow Exponentiated (Extended) Chen distribution with three parameters…

We introduce a family of quantum semigroups and their natural coactions on noncommutative polynomials. We present three invariance conditions, associated with these coactions, for the joint distribution of sequences of selfadjoint…

Let $\boldsymbol{X}$ be a $d$-dimensional random array on $[n]$ whose entries take values in a finite set $\mathcal{X}$, that is, $\boldsymbol{X}=\langle X_s:s\in \binom{[n]}{d}\rangle$ is an $\mathcal{X}$-valued stochastic process indexed…

We study random relational structures that are \emph{relatively exchangeable}---that is, whose distributions are invariant under the automorphisms of a reference structure $\mathfrak{M}$. When $\mathfrak{M}$ has {\em trivial definable…

We show that if X and Y are integers independently and uniformly distributed in the set {1, ..., N}, then the information lost in forming their product (which is given by the equivocation H(X,Y | XY)), is of order log log N. We also prove…

Multivariate extreme value theory assumes a multivariate domain of attraction condition for the distribution of a random vector. This necessitates that each component satisfies a marginal domain of attraction condition. An approximation of…

We characterize the class of exchangeable feature allocations assigning probability $V_{n,k}\prod_{l=1}^{k}W_{m_{l}}U_{n-m_{l}}$ to a feature allocation of $n$ individuals, displaying $k$ features with counts $(m_{1},\ldots,m_{k})$ for…

We prove that, for any jointly stable random variables $X_1, \dots, X_k$ with zero mean, any $m<k,$ and any even continuous positive definite functions $f$ and $g$ on $\Bbb R^m$ and $\Bbb R^{k-m},$ the random variables $f(X_1,\dots,X_m)$…

Let $Y$ be a nonnegative random variable with mean $\mu$ and finite positive variance $\sigma^2$, and let $Y^s$, defined on the same space as $Y$, have the $Y$ size biased distribution, that is, the distribution characterized by…