On the bounded binomial distribution and its parameter estimation

Abstract

In this paper, a modified binomial distribution is suggested to cope with situations in which some of the frequencies of a binomial distribution are not distinguishable from others, or the number of occurrence of the event is bounded by a number which is less than the total number of trials. Maximum likelihood estimator, moment estimator, and other estimators of the proportion parameter p are considered.

Keywords:

• asymptotic normality
• bounded multinomial distribution
• maximum likelihood estimator
• moment estimator
• consistency
• Monte Carlo simulation