| In this dissertation, we generalize the binomial distribution by relaxing independence to partial exchangeability and derive the distribution. By mixing this distribution with rectangular completely monotonic functions we obtain a new class of parsimonious distributions of multivariate parameter. We give several methods to obtain parsimonious distributions of any number of parameters. By applying these methods we present various such distributions. These distributions can be used to model correlated binary data. By allowing the parameters to depend on covariates we introduce a regression procedure. We discuss maximum likelihood estimation and give asymptotic normality. The proposed procedure is applied to fit real data consisting of binary sequences from the Ohio Agricultural Research and Development Center and a bladder cancer study by the Veterans Administration Cooperative Urological Research Group (VACURG). |
