The matching, birthday and the strong birthday problem: a contemporary review

@article{Dasgupta2005TheMB,
  title={The matching, birthday and the strong birthday problem: a contemporary review},
  author={Anirban Dasgupta},
  journal={Journal of Statistical Planning and Inference},
  year={2005},
  volume={130},
  pages={377-389}
}
  • A. Dasgupta
  • Published 2005
  • Mathematics
  • Journal of Statistical Planning and Inference
This article provides a contemporary exposition at a moderately quantitative level of the distribution theory associated with the matching and the birthday problems. A large number of examples, many not well known, are provided to help a reader have a feeling for these questions at an intuitive level. 

Tables from this paper

The Second-Moment Phenomenon for Monochromatic Subgraphs
TLDR
The celebrated birthday problem is a problem which can be formulated as the existence of a group of friends all of whom have the same birthday. Expand
The strong birthday problem
TLDR
This issue marks the tenth birthday of Significance magazine and Mario Cortina Borja examines the strong birthday problem, which aims to explain why birthday problems can be so serious. Expand
Methods for Studying Generalized Birthday and Coupon Collection Problems
TLDR
This paper considers generalizations of two classical probability problems: the birthday problem and the coupon collector's problem in terms of urn models and captured through generating functions. Expand
A factorial moment distance and an application to the matching problem
In this note we introduce the notion of factorial moment distance for non-negative integer-valued random variables and we compare it with the total variation distance. Furthermore, we study the rateExpand
A non-uniform birthday problem with applications to discrete logarithms
TLDR
This work considers a generalisation of the birthday problem that arises in the analysis of algorithms for certain variants of the discrete logarithm problem in groups, such that the distribution of assigning balls to urns depends on the colour of the ball. Expand
Simple Approximation Formulas for the Birthday Problem
TLDR
An easily computable approximation is suggested that allows an easy answer to the question of how many people are needed, so that the probability of at least two or three of n persons having the same birthday exceeds a given value. Expand
Fundamentals of Probability: A First Course
Introducing Probability.- The Birthday and Matching Problems.- Conditional Probability and Independence.- Integer-Valued and Discrete Random Variables.- Generating Functions.- Standard DiscreteExpand
The Birthday and Matching Problems
In this chapter, we offer a glimpse into some problems that have earned the status of being classics in counting and combinatorial probability. They have an entertainment value, and they also presentExpand
A Bayesian analysis of the matching problem
Abstract The matching problem is known since the beginning of the eighteenth century and Bayesian solutions have been proposed. In this paper, we present a Bayesian analysis of an experiment thatExpand
Counting birthday collisions using partitions.
We use partitions to provide some formulae for counting s-collisions and other events in various forms of the Birthday Problem.
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 34 REFERENCES
Extensions of the birthday surprise
Abstract The so-called “birthday surprise” is the fact that, on the average, one need only stop about 24 people at random to discover two who have the same birthday. Here we determine,Expand
Limit Distributions and Random Trees Derived from the Birthday Problem with Unequal Probabilities
Given an arbitrary distribution on a countable set, consider the number of independent samples required until the first repeated value is seen. Exact and asymptotic formulae are derived for theExpand
Variations on the Monotone Subsequence Theme of Erdös and Szekeres
A review is given of the results on the length of the longest increasing subsequence and related problems. The review covers results on random and pseudorandom sequences as well as deterministicExpand
Longest increasing subsequences: from patience sorting to the Baik-Deift-Johansson theorem
We describe a simple one-person card game, patience sorting. Its analysis leads to a broad circle of ideas linking Young tableaux with the longest increasing subsequence of a random permutation viaExpand
Problems and Snapshots from the World of Probability
TLDR
This book comprises a collection of 125 problems and snapshots from discrete probability that provide quick overviews of topics in probability such as Markov chains, Poisson processes, random walks, patterns in random sequences, cover times, and embedding procedures. Expand
Methods for studying coincidences
This article illustrates basic statistical techniques for studying coincidences. These include data-gathering methods (informal anecdotes, case studies, observational studies, and experiments) andExpand
Poisson Approximation and the Chen-Stein Method
The Chen-Stein method of Poisson approximation is a powerful tool for computing an error bound when approximating probabilities using the Poisson distribution. In many cases, this bound may be givenExpand
Natural sorting over permutation spaces
0. Introduction. In this paper we continue the study, begun in [1], of some combinatorial problems related to monotonicities that occur in certain spaces of finite sequences. These spaces areExpand
Problems in combinatorics and graph theory
Three hundred and sixty-nine problems with fully worked solutions for courses in computer science, combinatorics, and graph theory, designed to provide graded practice to students with as little as aExpand
Two moments su ce for Poisson approx-imations: the Chen-Stein method
Convergence to the Poisson distribution, for the number of occurrences of dependent events, can often be established by computing only first and second moments, but not higher ones. This remarkableExpand
...
1
2
3
4
...