Published online by Cambridge University Press: 14 July 2016
A sequence of independent, identically distributed random variables is observed. After a sample of m has been collected attention is fixed to a particular observation. In this paper the fluctuations of the rank of this observation, as sampling continues, will be studied.
The process can be modelled by a Pólya urn scheme, and new results are obtained which are of interest in both sequential rank and Pólya urn contexts.
Present address: Department of Applied Statistics, The University, Whiteknights, Reading RG6 2AN, U.K.