Binary choice modelling based on the universal distribution

The paper considers the problem of classification and some methods for its solution based on the binary choice models. Logit- and probit models have been preferred to discriminant function model because they are able to process different input data types. So, the question on the possible introduction of the new model based on the function, which differs from the logit function for the logit model and the normal function for probit model respectively, is considered. The mathematical model is fully described, the possibility of introduction of a new model is justified and the existing restrictions preventing this action are given. Moreover, a new method for evaluation of the parameters of the classification function, based on the universal distribution, is presented. It is proposed to take the general normal distribution as a new distribution with unknown parameters. The new classification procedure helps solve the dual optimization problem: minimization of the likelihood function with the optimal coefficients fitting for the classification function and minimization of the classification error magnitude by varying the parameters of the selected distribution. In order to test the new method, a set of computational experiments was performed with different sample sizes and varied number of income variables and various dependencies in the input data. The results were studied in detail in order to fix the influence of input data distribution on the probability model empirical distribution. The obtained results show the effectiveness of the proposed procedure. This is particularly well observed in the tests with the extended model (with a lot of variables). The possible ways of further development of the work are noted. Due to the fact, that the proposed method works well, it is possible to study the magnitude of the classification error by choosing any other statistical distribution for creating the models with the certain conditions in the future. It should be noted, that the new method for solving the classification problem significantly improves the classification quality of the existing procedures, so it can be successfully applied in practice.