Parametric estimation of extinction probability of branching process by using joint estimation of Mean and Variance

Parametric estimation of extinction probability of branching process

Abstract

The paper deals with the joint asymptotic normality of estimators of offspring mean and the offspring variance of the Bienayme-Galton-Watson Branching process, when n generation sizes are observable. Using these results, the probability of ultimate extinction is also estimated in the parametric set up. As an illustration, an application of the method to the case of fractional linear generating function is demonstrated. The method is also applied for H1N1 positive cases data generated during 2009.