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A Poisson limit theorem for incomplete symmetric statistics

Published online by Cambridge University Press:  14 July 2016

M. Berman  and
G. K. Eagleson
M. Berman*
Affiliation:
CSIRO Division of Mathematics and Statistics, Sydney
G. K. Eagleson*
Affiliation:
CSIRO Division of Mathematics and Statistics, Sydney
*
∗ Postal address: CSIRO Division of Mathematics and Statistics, P.O. Box 218, Lindfield NSW 2070, Australia.
∗ Postal address: CSIRO Division of Mathematics and Statistics, P.O. Box 218, Lindfield NSW 2070, Australia.
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Abstract

Silverman and Brown (1978) have derived Poisson limit theorems for certain sequences of symmetric statistics, based on a sample of independent identically distributed random variables. In this paper an incomplete version of these statistics is considered and a Poisson limit result shown to hold. The powers of some tests based on the incomplete statistic are investigated and the main results of the paper are used to simplify the derivations of the asymptotic distributions of some statistics previously published in the literature.

Keywords

M-DEPENDENT PROCESSPOINT PROCESSPOISSON PROCESSRANDOM COVERINGRENEWAL PROCESSSCAN STATISTIC
Type
Research Papers
Information
Journal of Applied Probability , Volume 20 , Issue 1 , March 1983 , pp. 47 - 60
Copyright
Copyright © Applied Probability Trust 1983 

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