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Abstract
In this thesis, we present approximations and bounds for the extinction probability π0 of a Galton-Watson branching process. The methods used include some modified Padé approximations as well as approximations of Hermite polynomial form. In a few cases, we generalize a few bounds previously published in the literature.
To compare the methods, we consider several different offspring or progeny distributions, including the Poisson, binomial and negative binomial distributions. Also considered are approximations based on negative moments, which have not been previously considered.
It is concluded that the bounds and approximations considered here, work best for means of offspring distributions of approximately 3.0 or less, and work less well otherwise, in most applications, means of offspring distributions larger than 1.0 but less than 2.0 are especially important, so the bounds and approximations given here should be useful.
