In this note we are concerned with the inflated-parameter binomial distribution, which is a generalization of the classical binomial distribution. We show that there exists exactly one renewal process such that the number of renewals has an inflated-parameter binomial distribution.

Here we develop an order k version of the zero-inflated logarithmic series distribution of Kumar and Riyaz [Staistica (accepted for publication), <CitationRef CitationID="CR10">2013b</CitationRef>] through its probability generating function, and derive an expression for its probability mass function. Certain recurrence relation for its...</citationref>