dc.description.abstract | The objective of this project is to study discrete probability distributions and their
recursive patterns.
In Chapter I, we state the importance of expressing probability distributions in terms of
recursive relations. This is because in some certain probability distributions it is often
easier to deal with the recursive relations rather than the distributions themselves in
obtaining the moments.
In Chapter II, we reviewed the various methods for determining discrete probability
distributions. Some of these methods include both the binomial and exponential
expansions, the Jacobian transformation (Change of Variable technique) .We also applied
the expectation and convolution approaches to sums of iid random variables to obtain the
resulting compound distributions.
In Chapter III, we have derived the recursive ratios and recursive relations for the various
probability distributions that have been identified in Chapter II. Using the recursive
relations, we have obtained the means and variances, based on the pgftechnique (where
possible) and Feller's method.
In Chapter IV, we reviewed a number of patterns of recursive relations; the main ones
being the Panj er (1981) and Willmot (1988) patterns. With these patterns, we have been
able to identify the corresponding probability distributions.
In Chapter V, we have reviewed-some maximum likelihood estimation procedures. We
have applied Sprott's procedure for deriving maximum likelihood equations.
Chapter VI contains the conclusions of this project and recommendations for further
research. | en |