Estimation of Entropy for Generalized Exponential Distribution Based on Record Values

  • Manoj Chacko
  • Asha P. S.
Research Article


In this paper, estimation of entropy for generalized exponential distribution based on record values is considered. Maximum likelihood estimation and Bayes estimation for Shannon entropy and Renyi entropy have been considered based on record values. Bayes estimators are obtained using importance sampling method. A simulation study is performed to find the performance of the estimators developed in this paper. Inferential procedures developed in this paper have also been illustrated using real data.


Entropy Record values Bayes estimators Importance sampling method 



The authors are grateful to the referees for their valuable comments and suggestions.


  1. Ahmadi J, Doostparast M (2006) Bayesian estimation and prediction for some life distributions based on record values. Stat Pap 47:373–392MathSciNetCrossRefzbMATHGoogle Scholar
  2. Ahsanullah M (1995) Record statistics. Nova Science Publishers, New YorkzbMATHGoogle Scholar
  3. Arnold BC, Balakrishnan N, Nagaraja HN (1998) Records. Wiley, New YorkCrossRefzbMATHGoogle Scholar
  4. Balakrishnan N, Chan PS (1998) On the normal record values and associated inference. Stat Prob Lett 39:73–80MathSciNetCrossRefzbMATHGoogle Scholar
  5. Baratpour S, Ahmadi J, Arghami NR (2007) Entropy properties of record statistics. Stat Pap 48:197–213MathSciNetCrossRefzbMATHGoogle Scholar
  6. Cramer E, Bagh C (2011) Minimum and maximum information censoring plans in progressive censoring. Commun Stat Theory Methods 40:2511–2527MathSciNetCrossRefzbMATHGoogle Scholar
  7. Chandler KN (1952) The distribution and frequency of record values. J Roy Stat Soc B 14:220–228MathSciNetzbMATHGoogle Scholar
  8. Chen MH, Shao QM (1999) Monte Carlo estimation of Bayesian credible and HPD intervals. J Comput Gr Stat 8:69–92MathSciNetGoogle Scholar
  9. Cho Y, Sun H, Lee K (2014) An estimation of the entropy for a Rayleigh distribution based on doubly-generalized Type-II hybrid censored samples. Entropy 16:3655–3669MathSciNetCrossRefzbMATHGoogle Scholar
  10. Cho Y, Sun H, Lee K (2015) Estimating the entropy of a Weibull distribution under generalized progressive hybrid censoring. Entropy 17:102–122CrossRefGoogle Scholar
  11. Kim C, Song S (2010) Bayesian estimation of the parameters of the generalized exponential distribution from doubly censored samples. Stat Pap 51:583–597MathSciNetCrossRefzbMATHGoogle Scholar
  12. Kundu D, Gupta RD (1999) Generalized exponential distribution. Aust NZ J Stat 41:173–188MathSciNetCrossRefzbMATHGoogle Scholar
  13. Kundu D, Gupta RD (2008) Generalized exponential distribution: Bayesian estimation. Comput Stat Data Anal 52:1873–1883MathSciNetCrossRefzbMATHGoogle Scholar
  14. Madi MT, Raqab MZ (2007) Bayesian prediction of rainfall records using the generalized exponential distribution. Environmetrics 18:541–549MathSciNetCrossRefGoogle Scholar
  15. Raqab MZ, Madi MT (2005) Bayesian inference for the generalized exponential distribution. J Stat Comput Simul 75:841–852MathSciNetCrossRefzbMATHGoogle Scholar
  16. Raqab MZ (2002) Inferences for generalized exponential distribution based on record statistics. J Stat Plan Inference 104:339–350MathSciNetCrossRefzbMATHGoogle Scholar
  17. Raqab MZ, Ahsanullah M (2001) Estimation of location and scale parameters of generalized exponential distribution based on order statistics. J Stat Comput Simul 69:109–124MathSciNetCrossRefzbMATHGoogle Scholar
  18. Kamps U (1994) Reliability properties of record values from non-identically distributed random variables. Commun Stat Theory Methods 23:2101–2112MathSciNetCrossRefzbMATHGoogle Scholar
  19. Kang SB, Cho YS, Han JT, Kim J (2012) An estimation of the entropy for a double exponential distribution based on multiply Type-II censored samples. Entropy 14:161–173MathSciNetCrossRefzbMATHGoogle Scholar
  20. Raqab M (2002) Inference for generalized exponential distribution based on record statistics. J Stat Plan Inference 104:339–350MathSciNetCrossRefzbMATHGoogle Scholar
  21. Renyi A (1961) On measures of entropy and information. In: Proceedings of the fourth Berkeley symposium on mathematics, statistics and probability. University of California Press, Berkeley, vol 1, pp 547–561Google Scholar
  22. Seo JI, Lee HJ, Kang SB (2012) Estimation for generalized half logistic distribution based on records. J Korean Data Inf Sci Soc 23:1249–1257Google Scholar
  23. Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27:379–432MathSciNetCrossRefzbMATHGoogle Scholar
  24. Sultan KS, Moshref ME, Childs A (2002) Record values from generalized power function distribution and associated inference. J Appl Stat Sci 11:143–156MathSciNetzbMATHGoogle Scholar

Copyright information

© The Indian Society for Probability and Statistics (ISPS) 2018

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of KeralaTrivandrumIndia

Personalised recommendations