A probabilistic generalization of Taylor's theorem

William A. Massey, Ward Whitt

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


We derive probabilistic generalizations of the fundamental theorem of calculus and Taylor's theorem, obtained by making the argument interval random. The remainder terms are expressed in terms of iterates of the familiar stationary-excess or equilibrium residual-lifetime distribution from the theory of stochastic point processes. The probabilistic generalization of Taylor's theorem can be applied to approximate the mean number of busy servers at any time in an Mt/G/∞ queueing system.

Original languageEnglish (US)
Pages (from-to)51-54
Number of pages4
JournalStatistics and Probability Letters
Issue number1
StatePublished - Jan 4 1993
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Taylor's theorem
  • fundamental theorem of calculus
  • infinite-server queues
  • nonstationary queues
  • residual lifetime
  • stationary-excess distribution
  • stochastic point processes


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