This dissertation explores the development of statistical methodology for some problems of branching processes and poisson shock model.

Branching process methods have become extremely popular in recent days. This dissertation mainly explores two fundamental inference problems of Galton-Watson processes. The first problem is concerned with statistical inference regarding the nature of the process. Two methodologies have been developed to develop a statistical test for the null hypothesis that the process is supercritical versus an alternative hypothesis that the process is non-supercritical. Another problem we investigate involves the estimation of the 'age' of a Galton-Watson Process. Three different methods are discussed to estimate the 'age' with suitable numerical illustrations. Computational aspects of these methods have also been explored.

The literature regarding non-parametric aging properties is quite extensive. Bhattacharjee (2005) recently introduced a new notion of non-parametric aging property known as Strong decreasing Failure rate (SDFR). This dissertation explores necessary and sufficient conditions for which this nonparametric aging property is preserved under Essary-Marshall-Proschan shock model. It has been proved that the discrete SDFR property is transmitted to continuous version of SDFR under a shock model operation. A counter example has been constructed to show that the converse is false.