Estimation of growth rate in second order branching process

- Estimation of growth rate for second order Bienaymé-Galton-Watson model is discussed.
- Consistency and asymptotic normality of the proposed estimator are established.
- Model is used to model the swine flu data for Pune, India and La-Gloria, Mexico.

The classical BGW process assumes first order dependence, whereas many real life datasets exhibit a second or higher order dependence. Further, in some situations, there is a need for a model which allows for simultaneous reproduction by a parent and its offspring. Kashikar and Deshmukh (2015) have proposed a second order Bienaymé-Galton-Watson (SOBGW) model to deal with such situations. This paper discusses estimation of growth rate for SOBGW model when only the generation sizes are observed. This model is further used to model the swine flu data for Pune, India and La-Gloria, Mexico.