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Research Article

Estimation of Rényi entropy for lifetime uncertainty

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Pages 1673-1690 | Received 19 Jun 2023, Accepted 19 Dec 2023, Published online: 29 Dec 2023

References

  • Shannon CE. A mathematical theory of communication. Bell Syst Tech J. 1948;27:379–423. doi: 10.1002/bltj.1948.27.issue-3
  • Rényi A. On measures of entropy and information. In: Proceedings of the fourth Berkeley Symposium on Mathematical Statistics and Probability. Berkeley, California, USA; 1961; p. 547–561.
  • Liitiainen E, Lendasse A, Corona F. On the statistical estimation of Rényi entropies. In: 2009 IEEE International Workshop on Machine Learning for Signal Processing. IEEE; 2009; p. 1–6.
  • Pál D, Póczos B, Szepesvári C. Estimation of Rényi entropy and mutual information based on generalized nearest-neighbor graphs. Adv Neural Inf Process Syst. 2010;23:1849–1857.
  • Maya R, Abdul-Sathar EI, Rajesh G, et al. Estimation of the Rényi's residual entropy of order α with dependent data. Stat Pap. 2014;55:585–602. doi: 10.1007/s00362-013-0506-1
  • Kayal S, Kumar S, Vellaisamy P. Estimating the Rényi entropy of several exponential populations. Braz J Probab Stat. 2015;29(1):94–111. doi: 10.1214/13-BJPS230
  • Acharya J, Orlitsky A, Suresh AT, et al. Estimating Rényi entropy of discrete distributions. IEEE Trans Inf Theory. 2016;63(1):38–56. doi: 10.1109/TIT.2016.2620435
  • Gilchrist W. Statistical modelling with quantile functions. London: Chapman and Hall/CRC; 2000.
  • Nair NU, Sankaran PG. Quantile-based reliability analysis. Commun Stat-Theory Methods. 2009;38:222–232. doi: 10.1080/03610920802187430
  • Nair NU, Sankaran PG, Balakrishnan N. Quantile-based reliability analysis. US: Springer; 2013.
  • Kayal S, Tripathy MR. A quantile-based Tsallis-α divergence. Phys A: Stat Mech Appl. 2018;492:496–505. doi: 10.1016/j.physa.2017.10.023
  • Kumar V, Dangi B. Quantile-based Shannon entropy for record statistics. Commun Math Stat. 2022;5:1–24. doi: 10.1007/s40304–021–00248–5
  • Nair NU, Vineshkumar B. Modelling informetric data using quantile functions. J Informetr. 2022;16(2):101266. doi: 10.1016/j.joi.2022.101266
  • Aswin IC, Sankaran PG, Sunoj SM. Some reliability aspects of record values using quantile functions. Commun Stat-Theory Methods. 2023. doi: 10.1080/03610926.2023.2189499
  • Nanda AK, Sankaran PG, Sunoj SM. Rényi's residual entropy: a quantile approach. Stat Probab Lett. 2014;85:114–121. doi: 10.1016/j.spl.2013.11.016
  • Nair NU, Sunoj SM, Rajesh G. Some new results on Renyi entropy and its relative measure. Calcutta Stat Assoc Bull. 2022;74(2):97–116. doi: 10.1177/00080683221137197
  • Leonenko N, Pronzato L, Savani V. A class of Rényi information estimators for multidimensional densities; 2008.
  • Jomhoori S, Yousefzadeh F. On estimating the residual Rényi entropy under progressive censoring. Commun Stat-Theory Methods. 2014;43(10-12):2395–2405. doi: 10.1080/03610926.2013.851219
  • Kayal S, Kumar S. Estimating Rényi entropy of several exponential distributions under an asymmetric loss function. REVSTAT-Stat J. 2017;15(4):501–522.
  • Chaubey YP, Sen PK. On smooth estimation of survival and density functions. Stat Risk Modeling. 1996;14:1–22. doi: 10.1524/strm.1996.14.1.1
  • Bagai I, Prakasa Rao B. Kernel-type density and failure rate estimation for associated sequences. Ann Inst Stat Math. 1995;47:253–266. doi: 10.1007/BF00773461
  • Jones MC. Estimating densities, quantiles, quantile densities and density quantiles. Ann Inst Stat Math. 1992;44:721–727. doi: 10.1007/BF00053400
  • Serfling RJ. On the strong law of large numbers and related results for quasi-stationary sequences. Theory Probab Its Appl. 1980;25:187–191. doi: 10.1137/1125022
  • Rao CR. On discrete distributions arising out of methods of ascertainment. Sankhya. 1965;27:311–324.
  • Soni P, Dewan I, Jain K. Nonparametric estimation of quantile density function. Comput Stat Data Anal. 2012;56:3876–3886. doi: 10.1016/j.csda.2012.04.014
  • Midhu NN, Sankaran PG, Nair NU. A class of distributions with linear hazard quantile function. Commun Stat-Theory Methods. 2014;43:3674–3689. doi: 10.1080/03610926.2012.705211
  • Al-Saiary ZA, Bakoban RA. The Topp-Leone generalized inverted exponential distribution with real data applications. Entropy. 2020;22:1144. doi: 10.3390/e22101144
  • Sheather SJ, Jones MC. A reliable data-based bandwidth selection method for kernel density estimation. J R Stat Soc Ser B (Methodol). 1991;53:683–690.
  • Hosking JRM. L-moments: analysis and estimation of distributions using linear combinations of order statistics. J R Stat Soc Ser B (Methodol). 1990;52:105–124.
  • Wang D, Hutson AD, Miecznikowski JC. L-moment estimation for parametric survival models given censored data. Stat Methodol. 2010;7(6):655–667. doi: 10.1016/j.stamet.2010.07.002
  • Nair NU, Subhash S, Sunoj S. Some new results on Cox–Czanner divergence and their applications in survival studies. Biom J Biom Z. 2022;65. doi: 10.1002/bimj.202200008
  • Kaplan EL, Meier P. Nonparametric estimation from incomplete observations. J Am Stat Assoc. 1958;53(282):457–481. doi: 10.1080/01621459.1958.10501452
  • Lawless JF. Statistical models and methods for lifetime data. New York: John Wiley & Sons; 2003.
  • Ebrahimi N. How to measure uncertainty in the residual life time distribution. Sankhya: Indian J Stat Ser A. 1996;58:48–57.

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