A probabilistic generalization of Taylor's theorem

William A. Massey; Ward Whitt

doi:10.1016/0167-7152(93)90122-Y

A probabilistic generalization of Taylor's theorem

William A. Massey, Ward Whitt

Research output: Contribution to journal › Article › peer-review

24 Scopus citations

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 M_t/G/∞ queueing system.

Original language	English (US)
Pages (from-to)	51-54
Number of pages	4
Journal	Statistics and Probability Letters
Volume	16
Issue number	1
DOIs	https://doi.org/10.1016/0167-7152(93)90122-Y
State	Published - Jan 4 1993
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Keywords

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

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10.1016/0167-7152(93)90122-Y

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AU - Massey, William A.

AU - Whitt, Ward

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N2 - 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.

AB - 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.

KW - Taylor's theorem

KW - fundamental theorem of calculus

KW - infinite-server queues

KW - nonstationary queues

KW - residual lifetime

KW - stationary-excess distribution

KW - stochastic point processes

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VL - 16

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EP - 54

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 1

ER -

A probabilistic generalization of Taylor's theorem

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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