A Note on Random Sums with Nonrandom Centering

P. S. Griffin

Journal of Theoretical Probability, 1997, vol. 10, issue 2, 333-348

Abstract: Abstract Let X 1, X 2,... be a sequence ofi.i.d. random variables and N n a sequence ofnon-negative integer valued random variables, independent of{X i }. The main results concern tightnessand weak convergence of $$(X_1 + \cdots + X_{N_n } - n\mu )\gamma _n^{ - 1} $$ under the natural condition that thesample mean is a consistent estimator of μ.

Keywords: Random sum; nonrandom centering; tightness; weak convergence; domain of attraction (search for similar items in EconPapers)
Date: 1997
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DOI: 10.1023/A:1022608415953

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