Related papers: Approximation Theorems Related to the Coupon Colle…
An information-theoretic development is given for the problem of compound Poisson approximation, which parallels earlier treatments for Gaussian and Poisson approximation. Let $P_{S_n}$ be the distribution of a sum $S_n=\Sumn Y_i$ of…
A Poisson Binomial distribution over $n$ variables is the distribution of the sum of $n$ independent Bernoullis. We provide a sample near-optimal algorithm for testing whether a distribution $P$ supported on $\{0,...,n\}$ to which we have…
In this paper, we study stochastic coupon probing problem in social networks. Assume there is a social network and a set of coupons. We can offer coupons to some users adaptively and those users who accept the offer will act as seeds and…
Constrained forest problems form a class of graph problems where specific connectivity requirements for certain cuts within the graph must be satisfied by selecting the minimum-cost set of edges. The prize-collecting version of these…
We extend the Coupon Collector's Problem (CCP) and present a novel generalized model, referred as the k-LCCP problem, where one is interested in recovering a bipartite graph with a perfect matching, which represents the coupons and their…
In many situations, sample data is obtained from a noisy or imperfect source. In order to address such corruptions, this paper introduces the concept of a sampling corrector. Such algorithms use structure that the distribution is purported…
The solution of the classical Coupon Collector's Problem is based on the assumptions that all stickers are independently and uniformly distributed. We can prove statistically as well as analytically that in particular the assumption of…
The Conway-Maxwell-Poisson (CMP) distribution is a natural two-parameter generalisation of the Poisson distribution which has received some attention in the statistics literature in recent years by offering flexible generalisations of some…
In "Recognizing the Maximum of a Sequence", Gilbert and Mosteller analyze a full information game where n measurements from an uniform distribution are drawn and a player (knowing n) must decide at each draw whether or not to choose that…
The (conditional or unconditional) distribution of the continuous scan statistic in a one-dimensional Poisson process may be approximated by that of a discrete analogue via time discretization (to be referred to as the discrete…
In applied probability, the normal approximation is often used for the distribution of data with assumed additive structure. This tradition is based on the central limit theorem for sums of (independent) random variables. However, it is…
This paper studies the sample complexity of searching over multiple populations. We consider a large number of populations, each corresponding to either distribution P0 or P1. The goal of the search problem studied here is to find one…
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…
Non-uniform estimates are obtained for Poisson, compound Poisson, translated Poisson, negative binomial and binomial approximations to sums of of m-dependent integer-valued random variables. Estimates for Wasserstein metric also follow…
We consider the problem of closeness testing for two discrete distributions in the practically relevant setting of \emph{unequal} sized samples drawn from each of them. Specifically, given a target error parameter $\varepsilon > 0$, $m_1$…
This paper investigates the asymptotic behavior of the Multi-set Allocation Occupancy (MAO) distribution, which models the count vector $X=(X_{=0},\ldots,X_{=T})$ from $T$ independent rounds of sampling without replacement of size $m$ from…
The classical Poisson theorem says that if $\xi_1,\xi_2,...$ are i.i.d. 0--1 Bernoulli random variables taking on 1 with probability $p_n\equiv \la/n$ then the sum $S_n=\sum_{i=1}^n\xi_i$ is asymptotically in $n$ Poisson distributed with…
A family of consistent tests, derived from a characterization of the probability generating function, is proposed for assessing Poissonity against a wide class of count distributions, which includes some of the most frequently adopted…
We propose a new method, probabilistic divide-and-conquer, for improving the success probability in rejection sampling. For the example of integer partitions, there is an ideal recursive scheme which improves the rejection cost from…
The paper is concerned with approximating the distribution of a sum W of n integer valued random variables Y_i, whose distributions depend on the state of an underlying Markov chain X. The approximation is in terms of a translated Poisson…