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NON-PARAMETRIC ESTIMATION FOR THE M/G/infinity QUEUE

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N. H. BINGHAM^{1} AND SUSAN M. PITTS^{2}

^{1} *Department of Mathematics and Statistics, Birkbeck College, University of London,*

Malet Street, London, WC1E 7HX, U.K.

^{2} *Department of Pure Mathematics and Mathematical Statistics, University of Cambridge,*

16 Mill Lane, Cambridge, CB2 1SB, U.K.
(Received November 7, 1996; revised October 17, 1997)

**Abstract.**
Given an *M*/*G*/*infinity* queue with input
rate *lambda* and service-time distribution *G*, we consider
the problem of estimating *lambda* and *G* from data on the
queue-length process *Q* = (*Q*_{t}). Our motivation is to study
departures of *G* from exponentiality, following recent work
of Bingham and Dunham (1997, *Ann. Inst. Statist.
Math.*, **49**, 667-679).

*Key words and phrases*:
Infinite-server queue,
infinite-dimensional delta-
method, empirical process, Little's formula, Reynolds'
formula.

**Source**
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