Advertisement

On Some Properties of Mathai–Haubold Entropy of Record Values

  • Jerin PaulEmail author
  • P. Yageen Thomas
Research Article
  • 1 Downloads

Abstract

In this article we consider Mathai–Haubold entropy and study some of its important properties based on record values. We derive some bounds and characterization results associated with the Mathai–Haubold entropy of record values. We further consider the Mathai–Haubold divergence measure and establish some its distribution free properties. We extend the concept of Mathai–Haubold entropy to the concomitants of record values arising from a Farlie–Gumbel–Morgenstern (FGM) family of bivariate distributions. Also we derive the expression and describe some properties of residual Mathai–Haubold entropy.

Keywords

Record values Mathai–Haubold entropy Maximum entropy principle Characterization Concomitants of record values Residual Mathai–Haubold entropy 

Notes

Acknowledgements

The authors express their gratefulness for the constructive comments of the learned referee which helped to improve considerably the revised version of the paper. The second author expresses his gratefulness to Kerala State Council for Science, Technology and Environment (DO No. 001/KESS/2015/KSCSTE dtd 17-12-2015) for supporting him financially in the form of Emeritus Scientist Award.

References

  1. Abbasnejad M, Arghami NR (2011) Renyi entropy properties of records. J Stat Plan Inference 141:2312–2320zbMATHGoogle Scholar
  2. Ahmadi J, Fashandi M (2012) Characterizations of symmetric distributions based on Renyi entropy. Stat Probab Lett 82:798–804zbMATHGoogle Scholar
  3. Anderson PE, Jensen HP, Oliveira LP, Sibani P (2004) Evolution in complex systems. Complexity 10(1):49–56MathSciNetGoogle Scholar
  4. Arnold BC, Balakrishnan N, Nagaraja HN (1998) Records. Wiley, New YorkzbMATHGoogle Scholar
  5. Baratpour S, Ahmadi J, Arghami NR (2007a) Entropy properties of record statistics. Stat Pap 48:197–213MathSciNetzbMATHGoogle Scholar
  6. Baratpour S, Ahmadi J, Arghami NR (2007b) Some characterizations based on entropy of order statistics and record values. Commun Stat Theory Methods 36(1):4757MathSciNetzbMATHGoogle Scholar
  7. Beck C (2006) Stretched exponentials from superstatistics. Phys A Stat Mech Appl 365(1):96–101Google Scholar
  8. Beck C, Cohen E (2003) Superstatistics. Phys A Stat Mech Appl 322:267–275MathSciNetzbMATHGoogle Scholar
  9. Chandler KN (1952) The distribution and frequency of record values. J R Stat Soc Ser B 14:220–228MathSciNetzbMATHGoogle Scholar
  10. Dar JG, Al-Zahrani B (2013) On some characterization results of life time distributions using Mathai–Haubold residual entropy. IOSR J Math 5(4):56–60Google Scholar
  11. Fashandi M, Ahmadi J (2012) Characterizations of symmetric distributions based on Renyi entropy. Stat Probab Lett 82(4):798–804zbMATHGoogle Scholar
  12. Goffman C, Pedrick G (1965) First course in functional analysis, 1st edn. Prentice Hall Inc, Upper Saddle RiverzbMATHGoogle Scholar
  13. Higgins JR (2004) Completeness and basis properties of sets of special functions, vol 72. Cambridge University Press, CambridgeGoogle Scholar
  14. Hwang J, Lin G (1984) On a generalized moment problem. II. Proc Am Math Soc 91(4):577–580MathSciNetzbMATHGoogle Scholar
  15. Johnson NL, Kotz S, Balakrishnan N (2002) Continuous multivariate distributions, models and applications, vol 1. Wiley, New YorkzbMATHGoogle Scholar
  16. Kerridge D (1961) Inaccuracy and inference. J R Stat Soc Ser B 28:184–194MathSciNetzbMATHGoogle Scholar
  17. Madadi M, Tata M (2014) Shannon information in k-records. Commun Stat Theory Methods 43(15):3286–3301MathSciNetzbMATHGoogle Scholar
  18. Majumdar SN, Ziff RM (2008) Universal record statistics of random walks and Levy flights. Phys Rev Lett 101(5):050601MathSciNetzbMATHGoogle Scholar
  19. Mathai A (2005) A pathway to matrix-variate gamma and normal densities. Linear Algebra Appl 396:317–328MathSciNetzbMATHGoogle Scholar
  20. Mathai A, Haubold H (2007a) On generalized entropy measures and pathways. Phys A Stat Mech Appl 385(2):493–500MathSciNetGoogle Scholar
  21. Mathai A, Haubold HJ (2007b) Pathway model, superstatistics, Tsallis statistics, and a generalized measure of entropy. Phys A Stat Mech Appl 375(1):110–122MathSciNetGoogle Scholar
  22. Mathai AM, Haubold HJ (2008) On generalized distributions and pathways. Phys Lett A 372(12):2109–2113zbMATHGoogle Scholar
  23. Minimol S, Thomas PY (2013) On some properties of Makeham distribution using generalized record values and its characterizations. Braz J Probab Stat 27(4):487–501MathSciNetzbMATHGoogle Scholar
  24. Minimol S, Thomas PY (2014) On characterization of Gompertz distribution by generalized record values. J Stat Theory Appl 13:38–45MathSciNetGoogle Scholar
  25. Nevzorov VB (2001) Records: mathematical theory. Translation of mathematical monographs, vol 194. American Mathematical Society, ProvidenceGoogle Scholar
  26. Paul J, Thomas PY (2013) On a property of generalized record values arising from exponential distribution. Indian Assoc Product Qual Reliab Trans 38:19–27Google Scholar
  27. Paul J, Thomas PY (2015) On generalized upper (k) record values from Weibull distribution. Statistica 75:313–330Google Scholar
  28. Paul J, Thomas PY (2016) Sharma-Mittal entropy properties on record values. Statistica 76:273–287Google Scholar
  29. Sebastian N (2015) Generalized pathway entropy and its applications in difiusion entropy analysis and fractional calculus. Commun Appl Ind Math 6(2):1–20Google Scholar
  30. Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27:379–423MathSciNetzbMATHGoogle Scholar
  31. Sibani P, Henrik JJ (2009) Record statistics and dynamics. In: Meyers RA (ed) Encyclopedia of complexity and systems science. Springer, New York, pp 7583–7591Google Scholar
  32. Thomas PY, Paul J (2014) On generalized lower (k) record values from the Frechet distribution. J Jpn Stat Soc 44(2):157–178MathSciNetzbMATHGoogle Scholar
  33. Zarezadeh S, Asadi M (2010) Results on residual Renyi entropy of order statistics and record values. Inf Sci 180(21):4195–4206zbMATHGoogle Scholar

Copyright information

© The Indian Society for Probability and Statistics (ISPS) 2019

Authors and Affiliations

  1. 1.Department of StatisticsVimala College (Autonomous)ThrissurIndia
  2. 2.Department of StatisticsUniversity of KeralaTrivandrumIndia

Personalised recommendations