Student Number : 9908888R -
MSc research report -
School of Statistics and Actuarial Science -
Faculty of Science / Much research has been devoted towards the understanding of population behaviour.
Such understanding has often been furthered through the development of theoretical
population models. This research report explores a variety of population models and
their implications.
The implications of the various models are explored using both analytical results and
simulations. Specific aspects of population behaviour studied include gross fluctuation
characteristics and extinction probabilities for a population.
This research report starts with an overview of Deterministic Models. This is followed
by a study of Birth and Death Processes, Branching Processes and Models that
incorporate environmental variability. Finally, we study the maximum likelihood
approach to population parameter estimation. The more notable theoretical results
derived include: the development of models that incorporate the population’s history;
models that incorporate discontinuous environmental changes and the development of
a means of parameter estimation for a Stochastic Differential Equation.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/2003 |
| Date | 15 February 2007 |
| Creators | Varughese, Melvin Mathew |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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