A distribution arising from a random walk on the plane / Sim Shin Zhu
2011
This thesis proposed a new distribution to model under-, equi- and overdispersion
in count data. It arises as a particular case of a modified random walk on the
plane, and includes the binomial, negative binomial and shifted negative binomial as
special cases. Some properties, test of hypothesis for equi-dispersion, simulation study
of power, parameter estimation by maximum likelihood and a squared distance method
based on the probability generating function are considered. The proposed distribution
is compared with existing distributions like the COM-Poisson and generalized Poisson
for modelling dispersion. It is shown to be a flexible model in applications by
illustrating its goodness-of-fit to four real data sets. In addition, two new bivariate
distributions are derived from proposed distribution as the alternative bivariate discrete
distributions by applying the convolution of two bivariate distributions and the classical
trivariate reduction method. It is found that the new bivariate distributions permit more
flexibility in modelling and less limitation on the correlation between the two random
variables. The characteristic and the estimation of the parameters of the new bivariate
distributions are provided. Furthermore, the statistical inference for the COM-Poisson
distribution and computational issues are studied. Test for equi-dispersion, study of
statistical power and parameter estimation by maximum likelihood are developed. This
thesis also considers a probability generating function-based divergence statistic for
parameter estimation. The performance and robustness of the proposed statistic in parameter estimation is studied for the negative binomial distribution by Monte Carlo simulation, especially in comparison with maximum likelihood and minimum Hellinger distance estimation.
Keywords:
- Econometrics
- Normal-gamma distribution
- Statistical parameter
- Beta-binomial distribution
- Exponential family
- Negative binomial distribution
- Statistics
- Inverse distribution
- Binomial distribution
- Mathematics
- Uniform distribution (continuous)
- Sampling distribution
- Quasi-likelihood
- Applied mathematics
- Univariate distribution
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