A central limit theorem for independent summands with infinite variances

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Abstract

A central limit theorem for independent summands having variances tending to infinity at a certain rate is obtained. This result is extended to the cases where the sample size is random and where the random variables are vector-valued.

Communicated by Dr. S. M. Shah,f.a.sc.
This research was supported by the National Science Foundation Grant NSF-GP 7847.