The thesis deals with models and statistical methodology for discrete count data, i.e. the data counting the numbers of events in discrete time periods. The basic model studied is the Poisson model with intensity depending on time and on a set of covariates. The model and methods of its statistical analysis are conpared with its continuos time parallel, the Cox's regresion model, equivalent large sample properties of estimates are proved. Several examples with unemployment data show the model application.