The Raybit Model and the Assessment of its Quality in Comparison with the Logit and Probit Models

Abstract

A new model for a dependent variable taking the value 0 or 1 (binary, dichotomous) was proposed. The name of the proposed model – the raybit model – stems from the fact that the probability corresponds to the Rayleigh cumulative distribution function. The assessment of the quality of selected models was conducted with the use of four definitions of error: MSE, MAE, WMSE, WMAE. Two computational examples were considered, which proved that the raybit model yields smaller values of error than the logit and probit models. Computer simulations were conducted using a random number generator with a binomial distribution. They proved that for the values of the theoretical probabilityfor the interval Pi ∈ [0; 0.8] the raybit model outperforms the other two models yielding a smaller value of error.