Estimation of discrete data using binomial mixture

Data analysis is an important method for obtaining information which is useful in many projects such as e.g. Smart Cities. Common data sources are questionnaires, their output mainly purveys discrete data. The most common description of discrete data is through categorical models. These models have several advantages such as flexibility but there are also disadvantages such as a huge dimension of the table expressing this distribution for more variables and values and their overparametrization. The aim of this paper is to replace the categorical distribution by another discrete distribution with a lower number of parameters while maintaining the model quality. Binomial distribution was chosen a suitable one because it is determined only by one parameter and this parameter allows to shape the probability function of binomial distribution well. The output of the paper is the presented model of mixture with binomial components. The suggested estimation algorithms are tested on real traffic data.