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Waiting time paradox and size biased sampling
Authors:Ramesh C. Gupta
Affiliation:University of Maine , Orono
Abstract:Feller's (1971) 'Waiting time for the bus paradox1 is explained by the fact that the long Interarrival times have a better chance of covering an arbitrary point in time than do short interarrival times, This gives rise to size biased sampling and the length of the Interarrival time that contains the arbitrary point has a moment distribution, This paper deals with the characterization of the exponential distribution based on this 'Waiting time paradox'. Similar characterizations of the binomial, the negative binomial, the Poisson and the geometric distributions are obtained.
Keywords:characterization of the exponential distribution  characterization of the negative binomial distribution  characterization of the binomial distribution  characterization of the Poisson distribution
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