Mixtures of Probability Distributions

Probability distributions are commonly used for modelling data governed by interval frequency distributions. The exact shape of a typical distribution of this kind is determined by the parameters of that distribution. In other words, our task is reduced to parameter estimation and, based on that, it is no problem to construct the exact shape of the distribution. A suitable model can thus be found for existing data, whether past or present. We show in our article that significantly better results can be achieved by using a mixture of probability distributions. This mixture can be formed in one of two ways. The first way is based on the unknown relevance of the observation to the component in the mixture, and the second way is based on the known relevance of the observation to the component in the mixture. We will use the latter and show the application of a mixture distribution with a different number of components in the mixture to the wage data in the Czech and Slovak Republics. Using time series analysis, we will also propose a way to predict future wage distributions in both countries.