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

Author

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  • A. Maron
  • M. Maron

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.

Suggested Citation

  • A. Maron & M. Maron, 2019. "Determination the Different Categories of Buyers Based on the Jaynes’ Information Principle," International Journal of Economics & Business Administration (IJEBA), International Journal of Economics & Business Administration (IJEBA), vol. 0(4), pages 336-342.
    • Handle: RePEc:ers:ijebaa:v:vii:y:2019:i:4:p:336-342
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    References listed on IDEAS

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    1. Sangkil Moon & Gary J. Russell, 2008. "Predicting Product Purchase from Inferred Customer Similarity: An Autologistic Model Approach," Management Science, INFORMS, vol. 54(1), pages 71-82, January.
    2. Kwak, Kyuseop & Duvvuri, Sri Devi & Russell, Gary J., 2015. "An Analysis of Assortment Choice in Grocery Retailing," Journal of Retailing, Elsevier, vol. 91(1), pages 19-33.
    3. Howard Smith, 2004. "Supermarket Choice and Supermarket Competition in Market Equilibrium," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(1), pages 235-263.
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    More about this item

    Keywords

    Statistical Decision Theory; Principle of Maximum Entropy; Marketing.;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • M31 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Marketing and Advertising - - - Marketing

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