Sequential rank and the Pólya urn
Herbert E. Robbins, John Whitehead · Journal of Applied Probability · 1979
A sequence of independent, identically distributed random variables is observed. After a sample ofmhas 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.