Related papers: Some Results on Joint Record Events

In probability theory, there is a tendency to treat one random variable with a given distribution as being just as good as any other. By and large this is fine because probability is (mostly) concerned with distributional properties of…

We study statistics of records in a sequence of random variables. These identical and independently distributed variables are drawn from the parent distribution rho. The running record equals the maximum of all elements in the sequence up…

Record linkage involves merging records in large, noisy databases to remove duplicate entities. It has become an important area because of its widespread occurrence in bibliometrics, public health, official statistics production, political…

This paper considers identification and estimation of distributional effect parameters that depend on the joint distribution of an outcome and another variable of interest ("treatment") in a setting with "two-sided" measurement error --…

We consider the occurrence of record-breaking events in random walks with asymmetric jump distributions. The statistics of records in symmetric random walks was previously analyzed by Majumdar and Ziff and is well understood. Unlike the…

Let ($X,Y)$ be a random vector with distribution function $F(x,y),$ and $(X_{1},Y_{1}),(X_{2},Y_{2}),...,(X_{n},Y_{n})$ are independent copies of ($X,Y).$ Let $X_{i:n}$ be the $i$th order statistics constructed from the sample…

For a random variable $N = 0, 1, 2, \ldots$ we study the following question: When does the sum of $N$ many independent and identically distributed copies of a random variable $X$ have the same law a a nontrivial rescaling of $X$? We show…

Let $q\ge2$ be an integer, $\{X_n\}_{n\geq 1}$ a stochastic process with state space $\{0,\ldots,q-1\}$, and $F$ the cumulative distribution function (CDF) of $\sum_{n=1}^\infty X_n q^{-n}$. We show that stationarity of $\{X_n\}_{n\geq 1}$…

In this paper, we establish a sufficient condition to compare linear combinations of independent and identically distributed (iid) infinite-mean random variables under usual stochastic order. We introduce a new class of distributions that…

We study asymptotic behavior of the moments $M_k(\lambda)$ of the sum $X_1+\dots+X_{N_\lambda}$, where $N_\lambda$ follows the Poisson probability distribution with mean value $\lambda$ and $\{X_j\}$ is a family of i.i.d. random variables…

We study the number of random records in an arbitrary split tree (or equivalently, the number of random cuttings required to eliminate the tree). We show that a classical limit theorem for convergence of sums of triangular arrays to…

Chain records is a new type of multidimensional record. We discuss how often the chain records are broken when the background sampling is from the unit cube with uniform distribution (or, more generally, from an arbitrary continuous product…

We introduce a class of stochastic integer sequences. In these sequences, every element is a sum of two previous elements, at least one of which is chosen randomly. The interplay between randomness and memory underlying these sequences…

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…

Given a set of several inputs into a system (e.g., independent variables characterizing stimuli) and a set of several stochastically non-independent outputs (e.g., random variables describing different aspects of responses), how can one…

The problem of quickest detection of a change in the distribution of a sequence of independent observations is considered. The pre-change observations are assumed to be stationary with a known distribution, while the post-change…

Rare events refer to qualitatively unlikely events whose realization can nevertheless have important consequences. Typically, the prediction of the kinetics of these events relies on Arrhenius laws, with exponentially distributed waiting…

For any physical observable in statistical systems, the most frequently studied quantities are its average and standard deviation. Yet, its full distribution often carries extremely interesting information and can be invoked to put any…

Understanding variable dependence, particularly eliciting their statistical properties given a set of covariates, provides the mathematical foundation in practical operations management such as risk analysis and decision-making given…

Let X_1,...., X_n be a collection of iid discrete random variables, and Y_1,..., Y_m a set of noisy observations of such variables. Assume each observation Y_a to be a random function of some a random subset of the X_i's, and consider the…