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On the Limiting Proportion of Types

Author

Listed:
  • Mark D. Rothmann

    (Georgia Institute of Technology)

  • Ralph P. Russo

    (University of Iowa)

Abstract

Consider a system into which units of random “type” enter at fixed points in time. Suppose each unit is endowed with a lifetime whose distribution is specific to its type, during which it is “active” (present in the system), and after which it is inactive (deleted from the system). Some unit types may tend to remain active for longer periods than others, and thus the limiting proportion of a given type within the active population may differ from the probability that an entering unit is of that type. The relation between the probabilities of types and the limiting proportion of types is shown to depend on the life distributions in a manner determined by the arrival time sequence.

Suggested Citation

  • Mark D. Rothmann & Ralph P. Russo, 1997. "On the Limiting Proportion of Types," Journal of Theoretical Probability, Springer, vol. 10(1), pages 131-143, January.
    • Handle: RePEc:spr:jotpro:v:10:y:1997:i:1:d:10.1023_a:1022698532576
    DOI: 10.1023/A:1022698532576
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    References listed on IDEAS

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    1. Rothmann, Mark D. & Russo, Ralph P., 1994. "Persistent convergence on randomly deleted sets," Statistics & Probability Letters, Elsevier, vol. 20(5), pages 367-373, August.
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    Cited by:

    1. Mark D. Rothmann & Ralph P. Russo, 2000. "Laws of Large Numbers for Observations that Change with Time," Journal of Theoretical Probability, Springer, vol. 13(4), pages 1013-1025, October.
    2. Z. Lin & X. Wang, 2004. "A Functional Limit Theorem for Observations That Change with Time," Journal of Theoretical Probability, Springer, vol. 17(4), pages 887-903, October.

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