A necessary and sufficient condition for convergence in law of random sums of random variables under nonrandom centering

Authors:
Mark Finkelstein and Howard G. Tucker

Journal:
Proc. Amer. Math. Soc. **107** (1989), 1061-1070

MSC:
Primary 60F05; Secondary 60G50

DOI:
https://doi.org/10.1090/S0002-9939-1989-0993749-9

MathSciNet review:
993749

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a sequence of independent, identically distributed (i.i.d.) random variables with common mean and variance . Let be a sequence of nonnegative integer-valued random variables such that for each the random variables are independent. Then if and only if , in which case the distribution of is that of , where and are independent random variables, being and having the same distribution as .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1989-0993749-9

Keywords:
Random sums of random variables,
nonrandom centering,
convergence in law

Article copyright:
© Copyright 1989
American Mathematical Society