Entropy as a Variation of Information for Testing the Goodness of Fit

  • Türkay Baran
  • Filiz Barbaros
  • Ali Gül
  • Gülay Onuşluel Gül


Increasing population, higher levels of human and industrial activities have affected water resources in the last decades. In addition, per capita demand for water in most countries is steadily increasing as more and more people achieve higher standards of living. Researchers need more information about water resources for their efficient use and effective management. In this respect, getting sufficient, accurate and quick information has great significance in water resources planning and management in parallel to the determination of the characteristics of water resources. To this end, useful and easily applicable methods have been explored to get optimum results and several test techniques have been investigated to get much more information based on available water resources data. In the presented study, Informational Entropy method is introduced as an alternative test method to test the goodness of fit of probability functions. The presented study gives a brief detail on the applicability of the concept as a goodness of fit tool on various cases from different spatial regions and varying meteorological characteristics. For this purpose, mean precipitation data for 60 stations in Turkey are investigated. Results by testing the goodness of fit of probability functions through the entropy-based method show that Informational Entropy can be applied for fitting the probability function based on the investigated datasets.


Informational entropy Probability analysis Trend analysis Goodness of fit Water resources 



A previous shorter version of the paper has been presented in the 10th World congress of EWRA “Panta Rei” Athens, Greece, 5–9 July 2017.

Compliance with Ethical Standards

Conflicts of Interest

The authors declare no conflict of interest.


  1. Abbas K, Alamgir, Khan SA, Khan DM, Ali A, Khalil U (2012) Modeling the distribution of annual maximum rainfall in Pakistan. Eur J Sci Res 79(3):418–429. ISSN 1450-216XGoogle Scholar
  2. Bacanli UG, Dikbas F, Baran T (2008) Drought analysis and a sample study of Aegean Region. 6th International conference on ethics and environmental policies, ItalyGoogle Scholar
  3. Baran T, Bacanli UG (2006) Evaluation of suitability criteria in stochastic modeling. European Water 13/14:35–43Google Scholar
  4. Baran T, Bacanli UG (2007a) An entropy approach for diagnostic checking in time series analysis. Water SA 33(4):487–496Google Scholar
  5. Baran T, Bacanli UG (2007b) Evaluation of goodness of fit criterion in time series analysis. Digest 2006 17:1089–1102Google Scholar
  6. Baran T, Barbaros F (2015) Testing the goodness of fit by informational entropy, European Water Resources Association 9th World Congress. Water resources management in a changing world: challenges and opportunities, June 10-13, 2015, Istanbul, CD of Proceedings, 7 p, Book of Abstracts, p 59Google Scholar
  7. Baran T, Barbaros F, Gul A, Onusluel Gul G (2017a) An informational entropy application to test the goodness of fit of probability functions. 10th World Congress of EWRA on Water Resources and Environment, ‘Panta Rhei’, 5-9 July 2017, Athens, Greece, Congress Proceedings, pp 403–408Google Scholar
  8. Baran T, Harmancioglu N, Cetinkaya CP, Barbaros F (2017b) An extension to the revised approach in the assessment of informational entropy. Entropy 19:634. CrossRefGoogle Scholar
  9. Best DJ, Rayner JCW, Thas O (2012) Comparison of some tests of fit for the inverse gaussian distribution. Advances in Decision Sciences, 2012:Article ID 150303, 9 pages. Hindawi Publishing Corporation.
  10. Cherry C (1957) On human communication: a review, a survey and a criticism. the Technology Press of Massachusetts Institute of Technology, Massachusetts, 333 pCrossRefGoogle Scholar
  11. DMI (2002) Turkish state meteorological service. Accessed 15 March 2017
  12. DMI (2016) Turkish state meteorological service. Accessed 1 March 2017
  13. Girardin V, Lequesne J (2017) Entropy-based goodness-of-fit tests—a unifying framework: application to DNA replication. Commun Stat Theor M.
  14. Guiasu S (1977) Information theory with applications. Mc Graw-Hill, New York. 439 p, ISBN 978-0070251090Google Scholar
  15. Harmancioglu N, Singh VP (1998) Entropy in environmental and water resources. In: Herschy RW, Fairbridge RW (eds) Encyclopedia of hydrology and water resources, vol 5. Kluwer Academic Publishers, Dordrecht, pp 225–241. ISBN 978-1-4020-4497-7CrossRefGoogle Scholar
  16. Harmancioglu N, Singh VP (2002) Data accuracy and data validation. In: Sydow A (ed) Encyclopedia of life support systems (EOLSS); knowledge for sustainable development, theme 11 on environmental and ecological sciences and resources, chapter 11.5 on environmental systems, vol 2. UNESCO Publishing-Eolss, Oxford, pp 781–798. ISBN 0 9542989-0-XGoogle Scholar
  17. Harmancioglu N, Singh VP, Alpaslan N (1992) Versatile uses of the entropy concept in water resources. In: Singh VP, Fiorentino M (eds) Entropy and energy dissipation in water resources, vol 9. Kluwer Academic Publishers, Dordrecht, pp 91–117. ISBN 978-94-011-2430-0CrossRefGoogle Scholar
  18. Jaynes ET (1983) In: Rosenkrantz RD (ed) Papers on probability, statistics and statistical physics. Springer, Dordrecht. 458 p, ISBN 978-94-009-6581-2Google Scholar
  19. Lee S, Vontab I, Karagrigoriou A (2011) A maximum entropy type test of fit. Comput Stat Data An 55:2635–2643CrossRefGoogle Scholar
  20. MGM (2017) Turkish state meteorological service. Accessed 10 Dec 2016
  21. Pfeiffer PE (1965) Concept of probability theory. McGraw-Hill Book Company, New York. 399 p, ISBN: 978-0486636771Google Scholar
  22. Pierce JR (1961) Symbols, signals and noise: the nature and process of communication. Harper and Row Publisher INC, New York. ISBN: 978-0061392320Google Scholar
  23. Shannon CE (1964) A mathematical theory of communication. In: Shannon, Weaver (eds) The mathematical theory of communication. The University of Illinois Press, UrbanaGoogle Scholar
  24. Shannon CE, Weaver W (1949) The mathematical theory of communication. University of Illinois Press, Urbana. 144 pGoogle Scholar
  25. Sharifdoost M, Nematollahi N, Pasha E (2009) Goodness of fit test and test of Independence by entropy. Journal of Mathematical Extension 3(2):43–59Google Scholar
  26. Singh VP (1997) The use of entropy in hydrology and water resources. Hydrol Process 11:587–626CrossRefGoogle Scholar
  27. Singh VP (1998) Entropy-based parameter estimation in hydrology. Kluwer Academic Publishers, Dordrecht. 364 pCrossRefGoogle Scholar
  28. Singh VP (2003) The entropy theory as a decision making tool in environmental and water resources. In: Karmeshu (ed) Entropy measures, maximum entropy principle and emerging applications. Studies in fuzziness and soft computing, vol 119. Springer, Berlin, pp 261–297. ISBN 978-3-540-36212-8CrossRefGoogle Scholar
  29. Weiss BA, Dardick W (2016) An entropy-based measure for assessing fuzziness in logistic regression. Educ Psychol Meas 76(6):986–1004CrossRefGoogle Scholar
  30. Zeng X, Wang D, Wu J (2015) Evaluating the three methods of goodness of fit test for frequency analysis. Journal of Risk Analysis and Crisis Response 5(3):178–187CrossRefGoogle Scholar

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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Faculty of Engineering, Department of Civil EngineeringDokuz Eylul UniversityIzmirTurkey

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