The Girl and the Birthday Problem

10.1142/12675 ◽  
2022 ◽  
Author(s):  
Boaz ◽  
Nicodemus Loh ◽  
Yit Wah Chang
Keyword(s):  
Birthday Problem

scholarly journals On the birthday problem: some generalizations and applications

2003 ◽  
Vol 2003 (60) ◽  
pp. 3827-3840 ◽  
Author(s):  
P. N. Rathie ◽  
P. Zörnig
Keyword(s):  
Probability Distribution ◽  
Random Graph ◽  
Generating Functions ◽  
Hypergeometric Functions ◽  
Exact Probability ◽  
Confluent Hypergeometric Functions ◽  
Birthday Problem ◽  
Exact Probability Distribution

We study the birthday problem and some possible extensions. We discuss the unimodality of the corresponding exact probability distribution and express the moments and generating functions by means of confluent hypergeometric functionsU(−;−;−)which are computable using the software Mathematica. The distribution is generalized in two possible directions, one of them consists in considering a random graph with a single attracting center. Possible applications are also indicated.

The Birthday Problem Revisited

1976 ◽  
Vol 7 (4) ◽  
pp. 39 ◽  
Author(s):  
Joe Dan Austin
Keyword(s):  
Birthday Problem

Poisson approximation for a sum of dependent indicators: an alternative approach

2002 ◽  
Vol 34 (03) ◽  
pp. 609-625 ◽  
Author(s):  
N. Papadatos ◽  
V. Papathanasiou
Keyword(s):  
Total Variation ◽  
Upper Bound ◽  
Random Variables ◽  
Random Variable ◽  
Poisson Approximation ◽  
Total Variation Distance ◽  
Poisson Random Variable ◽  
Birthday Problem ◽  
Alternative Approach ◽  
Variation Distance

The random variablesX1,X2, …,Xnare said to be totally negatively dependent (TND) if and only if the random variablesXiand ∑j≠iXjare negatively quadrant dependent for alli. Our main result provides, for TND 0-1 indicatorsX1,x2, …,Xnwith P[Xi= 1] =pi= 1 - P[Xi= 0], an upper bound for the total variation distance between ∑ni=1Xiand a Poisson random variable with mean λ ≥ ∑ni=1pi. An application to a generalized birthday problem is considered and, moreover, some related results concerning the existence of monotone couplings are discussed.

Seeing Double Voting: An Extension of the Birthday Problem

2008 ◽  
Vol 7 (2) ◽  
pp. 111-122 ◽  
Author(s):  
Michael P. McDonald ◽  
Justin Levitt
Keyword(s):  
Birthday Problem

Empirical Approaches to the Birthday Problem

2012 ◽  
Vol 106 (2) ◽  
pp. 132-137 ◽  
Author(s):  
Alfinio Flores ◽  
Kevin M. Cauto
Keyword(s):  
Random Numbers ◽  
Birthday Problem ◽  
Empirical Approaches

Experiments with random numbers give a new twist to this familiar problem.

A Note on the Inverse Birthday Problem With Applications

2017 ◽  
Vol 71 (3) ◽  
pp. 191-201 ◽  
Author(s):  
Wen-Han Hwang ◽  
Richard Huggins ◽  
Lu-Fang Chen
Keyword(s):  
Birthday Problem

A Direct Attack on a Birthday Problem

1976 ◽  
Vol 49 (3) ◽  
pp. 130-131
Author(s):  
Samuel Goldberg
Keyword(s):  
Birthday Problem ◽  
Direct Attack

THE ANALYSIS OF SINGLETONS IN GENERALIZED BIRTHDAY PROBLEMS

2012 ◽  
Vol 26 (2) ◽  
pp. 245-262 ◽  
Author(s):  
Matthijs R. Koot ◽  
Michel Mandjes
Keyword(s):  
Iterative Scheme ◽  
Demographic Data ◽  
Homogeneous Distribution ◽  
Birthday Problem ◽  
Mean And Variance ◽  
The Mean ◽  
The Impact

This paper describes techniques to characterize the number of singletons in the setting of the generalized birthday problem, that is, the birthday problem in which the birthdays are non-uniformly distributed over the year. Approximations for the mean and variance presented which explicitly indicate the impact of the heterogeneity (expressed in terms of the Kullback–Leibler distance with respect to the homogeneous distribution). Then an iterative scheme is presented for determining the distribution of the number of singletons. The approximations are validated by experiments with demographic data.

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