A Generalized Inflated Poisson Distribution

Count data with excess number of zeros, ones or twos are commonly encountered in experimental situations. In this thesis we have examined one such fertility data from Sweden. The standard Poisson distribution, which is widely used to model such count data, may not provide a good fit to model women\u27s fertility (defined as the number of children per woman in her lifetime) in a specific population due to various cultural and sociological reasons. Therefore, the usual Poisson distribution is inflated at specific values suitably, as dictated by the societal norms, to fit the available data. The data set is examined using various tests and techniques to determine the validity of using a multi-point inflated Poisson distribution as compared to the standard Poisson distribution. The various tests and techniques used include comparing the method of moment estimator of various multi-point inflated Poisson distributions along with the standard Poisson distribution. The maximum-likelihood estimators for Poisson distributions are also found and compared. Using simulation study, the maximum-likelihood and method of moment estimators were compared, and the maximum-likelihood estimator was found to have an overall better performance. Validation for the results found involves using the Chi-square goodness of fit test on the various Poisson distributions. Another validation test involves comparing the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) of the various Poisson distributions. The results of the various tests and techniques demonstrate that a multi-point inflated Poisson distribution provides a better fit and model as compared to the standard Poisson distribution