Related papers: Sampling from a mixture of different groups of cou…
We consider a generalisation of the classical coupon collector problem. We define a super-coupon to be any $s$-subset of a universe of $n$ coupons. In each round, a random $r$-subset from the universe is drawn and all its $s$-subsets are…
The Coupon Collector Problem (CCP) is a well-known combinatorial problem that seeks to estimate the number of random draws required to complete a collection of $n$ distinct coupon types. Various generalizations of this problem have been…
Let $V$ be an $n$-set, and let $X$ be a random variable taking values in the powerset of $V$. Suppose we are given a sequence of random coupons $X_1, X_2, \ldots $, where the $X_i$ are independent random variables with distribution given by…
The sequential sampling of populations with unequal probabilities and with replacement in a closed population is a recurrent problem in ecology and evolution. Many of these questions can be reformulated as urn problems, often as special…
We address a conjecture of Schilling concerning the optimality of the uniform distribution in the generalized Coupon Collector's Problem (CCP) where, in each round, a subset (package) of $s$ coupons is drawn from a total of $n$ distinct…
In the coupon collector problem with $n$ items, the collector needs a random number of tries $T_n\simeq n\ln n$ to complete the collection. Also, after $nt$ tries, the collector has secured approximately a fraction…
A popular variant of the collector's problem is the following: Assume there are $N$ different types of coupons with equal occurring probabilities. There is one main collector who collects coupons. When she gets a "double," she gives it to…
In order to identify the infected individuals of a population, their samples are divided in equally sized groups called pools and a single laboratory test is applied to each pool. Individuals whose samples belong to pools that test negative…
We initiate the study of the Careless Coupon Collector's Problem (CCCP), a novel variation of the classical coupon collector, that we envision as a model for information systems such as web crawlers, dynamic caches, and fault-resilient…
We study pairs and m--tuples of compositions of a positive integer n with parts restricted to a subset P of positive integers. We obtain some exact enumeration results for the number of tuples of such compositions having the same number of…
We consider the problem of estimating the number of types in a corpus using the number of types observed in a sample of tokens from that corpus. We derive exact and asymptotic distributions for the number of observed types, conditioned upon…
We consider the problem of choosing the best of $n$ samples, out of a large random pool, when the sampling of each member is associated with a certain cost. The quality (worth) of the best sample clearly increases with $n$, but so do the…
In this paper the coupon collector's problem with group drawings is studied. Assume there are $ n $ different coupons. At each time precisely $ s $ of the $ n $ coupons are drawn, where all choices are supposed to have equal probability.…
In this note we evaluate the expectation and variance of the waiting time to complete $m$ parallel collections of coupons, in the case of coupons which arrives independently, one by one and with equal probabilities.
Specimens are collected from $N$ different sources. Each specimen has probability $p$ of being contaminated, independently of the other specimens. We assume group testing is applicable, namely one can take small portions from several…
Let $N_n=\{1,2,...,n\}$. Elements are drawn from the set $N_n$ with replacement, assuming that each element has probability $1/n$ of being drawn. We determine the limiting distributions for the waiting time until the given portion of pairs…
Data scientists often draw on multiple relational data sources for analysis. A standard assumption in learning and approximate query answering is that the data is a uniform and independent sample of the underlying distribution. To avoid the…
We consider the combinatorial problem where $p$ players aim to a complete set of $N$ different types of items (species) which are uniformly distributed. Let the random variables $T_{N(i)},\,\,i=1,2,\cdots,p$ denoting the number of trials…
Computer-based tests with randomly generated questions allow a large number of different tests to be generated. Given a fixed number of alternatives for each question, the number of tests that need to be generated before all possible…
The usual problem for group testing is this: For a given number of individuals and a given prevalence, how many tests T* are required to find every infected individual? In real life, however, the problem is usually different: For a given…