On some properties and applications of quasi-binomial distribution

The observed counts generated in many experiments in nature by a set of Bernoulli type trials do not fit a binomial model and exhibit either much greater or much smaller variation than that of the binomial model. This is due to the extra effort exerted by the living beings and/or the special conditions faced by them. To accomodate such situations the binomial model has been generalized in different ways. For the same purpose Consul (1974) described an urn model which gave the Quasibinomial distribution (QBD). The QBD was found to be useful for many characterizations. Recently Berg and Mustafchiev (1988) have shown that the QBD is useful in random mappings with an attracting centre. In this paper we show that the QBD is a very versatile model and has many interesting properties. We consider its moments and maximum likelihood estimation and apply it to a number of observed data sets.