A Generalization of Weak Law of Large Numbers

Abstract

Kolmogorov's weak law of large numbers for i.i.d. random variables is generalized to a larger class distributions and to a wide class of normalizing sequences. The result is extended to maximal sums of negatively associated identically distributed random variables.

Keywords:

• Kolmogorov's weak law of large numbers
• Negatively associated and independent random variables
• Slowly varying function

Mathematics Subject Classification:

• 60F15
• 60G50

Acknowledgments

Research supported by the Russian Foundation for Basic Research, project 11-01-00515-a.

The author is grateful to professor M. M. Rao and an anonymous referee for helpful comments that lead to a better presentation of the results.