Likelihood Ratio And A Class of Limit Theorems Represented by Inequality for the Sequence of Integer-valued Random Variables

In this paper, the notion of likelihood ratio, as a measure of deviation between a sequence of the integer-valued random variables and a sequence of independent random variables with negative binomial distribution, is introduced. A subset of the sample space is given by restricting the likelihood ratio, and on this subset a class of limit theorems, represented by inequalities, for the sequence of arbitrary integer-valued random variables are obtained.