On the Limit of the Generalized Binomial Distribution

ABSTRACT

In this article we investigate the limit of the Generalized Binomial Distribution that results from correlated Bernoulli processes as the number of trials goes to infinity. For a correlation factor less than or equal to one half, we show, under certain assumptions, that the limit distribution is the standardized normal. For a correlation factor greater than one half, we find empirically that the limit is different from the standardized normal distribution.

Keywords:

• Central limit theorem
• Correlated Bernoulli events
• Generalized binomial

Mathematics Subject Classification:

• 60E99
• 62E20
• 62H10