Consistency of a Mixture Model of Two Different Distributions Approach to the Analysis of Buying Behaviour Data

Abstract

A four-parameter probability distribution, which includes a wide variety of curve shapes, is presented. Because of the flexibility, generality, and simplicity of the distribution, it is useful in the representation of data when the underlying model is unknown. Further important applications of the distribution include the modeling and subsequent generation of random variates for simulation studies and Monte Carlo sampling studies of the robustness of statistical procedures. This research centered on combining these two distributions that will simultaneously capture the rate of occurrence of a phenomenon, especially buying behaviour and the actual performance of that phenomenon as well as tracking and forecasting future purchasing pattern based the data. Further important applications of the distribution include the modeling and subsequent generation of random variates for simulation studies of the robustness of statistical procedures. To do this, specification of the hybrid model named Exponential- Gamma mixture model is given and followed by its derivation. The concluding part of the paper depicts an example of the areas of its application.