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1 results

  • Asymptotic probabilities in a sequential urn scheme related to the matchbox problem

  • Part of
  • Wolfgang Stadje
  • Journal:
    Advances in Applied Probability / Volume 30 / Issue 3 / September 1998
    Published online by Cambridge University Press:
    01 July 2016, pp. 831-849
    Print publication:
    September 1998

  • Generalizing the classical Banach matchbox problem, we consider the process of removing two types of ‘items’ from a ‘pile’ with selection probabilities for the type of the next item to be removed depending on the current numbers of remaining items, and thus changing sequentially. Under various conditions on the probability pn1,n2 that the next removal will take away an item of type I, given that n1 and n2 are the current numbers of items of the two types, we derive asymptotic formulas (as the initial pile size tends to infinity) for the probability that the items of type I are completely removed first and for the number of items left. In some special cases we also obtain explicit results.