Determination the Different Categories of Buyers Based on the Jaynes’ Information Principle

A. Maron, M. Maron
International Journal of Economics & Business Administration, Volume VII, Issue 4, 336-342, 2019

Abstract:

Purpose: The article aims to reduce the volume of statistical data, necessary for determination the buyer’s structure. The correct clustering of clients is important for successful activity for both commercial and non-profit organizations. This issue is devoted to a large number of studies. Their main mathematical apparatus is statistical methods. Input data are results of buyer polls. Polls are labor-consuming and quite often annoying buyers. The problem of determination of structure (various categories) of buyers by the mathematical methods demanding a small amount of these polls is relevant. Design/Methodology/Approach: The approach offered in this report based on the Jaynes' information principle (principle of maximum entropy). Jaynes idea is as follows. Let us consider a system in which the conditions cannot be calculated or measured by an experiment. However, each state of the system has a certain measured implication, the average value of which is known (or can be defined), and the average result of these implications is known from the statistical data. Then the most objective are probabilities of states maximizing Shannon’s entropy under restrictions imposed by information about average implications of states. Findings: In this work the task of determination of percentage of buyers for computer shop by the average check is set and solved provided that average checks for each concrete category of buyers are known. Input data for calculation are their average checks. Determination of these values requires much less statistical data, than to directly determine relative number of buyers of various categories. Practical Implications: The results are of particular interest to marketing experts. Originality/Value: The article deals with practical situation when initially there are only three different groups of customers. For this case, the problem of maximizing entropy under given constraints reduced to the problem of finding a solution to a system of three equations, of which only one is nonlinear. This is a completely new result.


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