Parameter estimation for strict arcsine distribution

Abstract

The two-parameter strict arcsine distribution as a member of the natural exponential family with cubic variance function has been shown to be a viable candidate for statistical analysis of count data. Efficient methods of parameter estimation will be essential in practical applications of the distribution. In this paper we examine some methods of parameter estimation. Due to the simple expression of the probability generating function, a probability generating function-based estimation procedure is considered and compared with other estimation procedures. Since the accuracy of the parameter estimation procedure affects the probability of correct selection in choosing the correct probability distribution, we extend the investigation by examining the discrimination between strict arcsine and generalized Poisson distributions in which both have cubic variance functions.