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International Journal of Mathematical Research

February 2016, Volume 5, 2, pp 179-187

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

Akomolafe Abayomi. A

Akomolafe Abayomi. A 1

  1. Department of Statistics, Federal University of Technology, Akure, Nigeria 1

on Google Scholar
on PubMed

Pages: 179-187

DOI: 10.18488/journal.24/2016.5.2/

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Article History:

Received: 19 December, 2015
Revised: 27 January, 2016
Accepted: 19 September, 2016
Published: 08 November, 2016


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.
Contribution/ Originality
This study contributes to the existing literature by combining exponential-gamma mixture as a hybrid model to see its rate of tracking and forecasting purchasing pattern. This is carried out by using our newly arrived formula in analyzing both the real life and simulated data in other to ascertain the uniqueness of combined probability distribution in forecasting future customer buying behavior data for producers effective planning and administration.


Data fitting, Probability distribution, Timing process, Exponential – gamma model, Buying behavior, Nonstationarity.



  1. A. A. Akomolafe, "Analysis of consumer depth of repeat purchasing pattern: An exploratory study of beverages buying behaviour data," Journal of Business and Organisational Development, vol. 3, pp. 1-8, 2011.
  2. M. G. Kendall and S. Alan, The advanced theory of statistics, 3rd ed. New York: Hafner, 1977.


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This study received no specific financial support.

Competing Interests:

The author declares that there are no conflicts of interests regarding the publication of this paper.


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