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A probabilistic generalization of Taylor's theorem

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  • Massey, William A.
  • Whitt, Ward

Abstract

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/[infinity] queueing system.

Suggested Citation

  • Massey, William A. & Whitt, Ward, 1993. "A probabilistic generalization of Taylor's theorem," Statistics & Probability Letters, Elsevier, vol. 16(1), pages 51-54, January.
    • Handle: RePEc:eee:stapro:v:16:y:1993:i:1:p:51-54
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    Cited by:

    1. Willmot, Gordon E., 1997. "Bounds for compound distributions based on mean residual lifetimes and equilibrium distributions," Insurance: Mathematics and Economics, Elsevier, vol. 21(1), pages 25-42, October.

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