Log in

Bivariate dynamic weighted cumulative residual entropy

  • Original Paper
  • Published:
Japanese Journal of Statistics and Data Science Aims and scope Submit manuscript

Abstract

As a way to measure uncertainty, the cumulative residual entropy (CRE) was initially developed. Later came the dynamic version of CRE, called dynamic cumulative residual entropy (DCRE). The bivariate dynamic cumulative residual entropy (BDCRE), a more sophisticated version of this measure, was also presented. In this study, we introduce and investigate the features of a weighted version of BDCRE.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (France)

Instant access to the full article PDF.

Fig. 1

Similar content being viewed by others

Data Availability

The dataset used and analyzed in our study is sourced from Kulkarni and Rattihalli (2002), and it is publicly available at https://www.jstor.org/stable/3085731.

References

  • Asadi, M., & Zohrevand, Y. (2007). On the dynamic cumulative residual entropy. Journal of Statistical Planning and Inference, 137, 1931–1941.

    Article  MathSciNet  Google Scholar 

  • Belis, M., & Guiasu, S. (1968). A quantitative-qualitative measure of information in cybernetic systems (corresp). IEEE Transactions on Information Theory, 14, 593–594.

    Article  Google Scholar 

  • Belzunce, F., Navarro, J., Ruiz, J. M., & Aguila, Y. D. (2004). Some results on residual entropy function. Metrika, 59, 147–161.

    Article  MathSciNet  Google Scholar 

  • Di Crescenzo, A., & Longobardi, M. (2006). On weighted residual and past entropies. Scientiae Mathematicae Japonicae, 64(3), 255–266.

    MathSciNet  Google Scholar 

  • Ebrahimi, N. (1996). How to measure uncertainty in the residual life time distribution. Sankhyā: The Indian Journal of Statistics, Series A, 58(1), 48–56.

  • Ebrahimi, N., Kirmani, S., & Soofi, E. S. (2007). Multivariate dynamic information. Journal of Multivariate Analysis, 98, 328–349.

    Article  MathSciNet  Google Scholar 

  • Ebrahimi, N., & Pellerey, F. (1995). New partial ordering of survival functions based on the notion of uncertainty. Journal of Applied Probability, 32(1), 202–211.

    Article  MathSciNet  Google Scholar 

  • Fisher, R. A. (1934). The effect of methods of methods of ascertainment up on the estimation of frequencies. Annals of Huan Genetics, 6, 13–25.

    Google Scholar 

  • Geetha, K. G., & Nair, V. K. R. (1998). A family of bivariate distribution useful in reliability modelling. Statistical Methods in Quality and Reliability, Educational Publishers and distributors, New Delhi, pp. 50–58.

  • Guiasu, S. (1986). Maximum entropy condition in queueing theory. Journal of the Operational Research Society, 37(3), 293–301.

    Article  Google Scholar 

  • Kawakami, R., Michimae, H., & Lin, Y.-H. (2021). Assessing the numerical integration of dynamic prediction formulas using the exact expressions under the joint frailty-copula model. Japanese Journal of Statistics and Data Science, 4(2), 1293–1321.

    Article  MathSciNet  Google Scholar 

  • Khammar, A., & Jahanshahi, S. (2018). On weighted cumulative residual tsallis entropy and its dynamic version. Physica A: Statistical Mechanics and its Applications, 491, 678–692.

    Article  MathSciNet  Google Scholar 

  • Kulkarni, H. V., & Rattihalli, R. (2002). Nonparametric estimation of a bivariate mean residual life function. Journal of the American Statistical Association, 97(459), 907–917.

    Article  MathSciNet  Google Scholar 

  • Lin, Y.-H., Sun, L.-H., Tseng, Y.-J., & Emura, T. (2022). The Pareto type I joint frailty-copula model for clustered bivariate survival data. Communications in Statistics-Simulation and Computation. https://doi.org/10.1080/03610918.2022.2066694

    Article  Google Scholar 

  • Mirali, M., Baratpour, S., & Fakoor, V. (2017). On weighted cumulative residual entropy. Communications in Statistics-Theory and Methods, 46(6), 2857–2869.

    Article  MathSciNet  Google Scholar 

  • Nair Rohini, S., & Abdul Sathar, E. I. (2019). Bivariate dynamic weighted survival entropy of order alpha. Stochastics and Quality Control, 34(2), 67–85.

    Article  MathSciNet  Google Scholar 

  • Navarro, J., Del Aguila, Y., & Ruiz, J. (2001). Characterizations through reliability measures from weighted distributions. Statistical Papers, 42, 395–402.

    Article  MathSciNet  Google Scholar 

  • Navarro, J., Sunoj, S. M., & Linu, M. N. (2014). Characterizations of bivariate models using some dynamic conditional information divergence measures. Communications in Statistics-Theory and Methods, 43, 1939–1948.

    Article  MathSciNet  Google Scholar 

  • Noughabi, M. S., & Kayid, M. (2019). Bivariate quantile residual life: A characterization theorem and statistical properties. Statistical Papers, 60(6), 2001–2012.

    Article  MathSciNet  Google Scholar 

  • Nourbakhsh, M., & Yari, G. (2017). Weighted Renyi’s entropy for lifetime distributions. Communications in Statistics-Theory and Methods, 46(14), 7085–7098.

    Article  MathSciNet  Google Scholar 

  • Rajesh, G., Abdul-Sathar, E., Nair, K.M., & Reshmi, K. (2014). Bivariate extension of dynamic cumulative residual entropy. Statistical Methodology, pp. 72–82.

  • Rao, C. R. (1965). On discrete distributions arising out of methods of ascertainment. Sankhyā: The Indian Journal of Statistics, Series A, 27, 311–324.

    MathSciNet  Google Scholar 

  • Rao, M., Chen, Y., Vemuri, B. C., & Wang, F. (2004). Cumulative residual entropy: A new measure of information. IEEE Transactions on Information Theory, 50, 1220–1228.

    Article  MathSciNet  Google Scholar 

  • Shannon, C. (1948). A mathematical theory of communication. Bell System Technical Journal, 27, 379-423 and 623–656. Mathematical Reviews (MathSciNet): MR10, 133e.

  • Shewa, F., Endale, S., Nugussu, G., Abdisa, J., Zerihun, K., & Banbeta, A. (2022). Time to kidneys failure modeling in the patients at adama hospital medical college: application of copula model. Journal of Research in Health Sciences, 22(2), e00549.

    Article  Google Scholar 

  • Wang, Y.-C., & Emura, T. (2021). Multivariate failure time distributions derived from shared frailty and copulas. Japanese Journal of Statistics and Data Science, 4(2), 1105–1131.

    Article  MathSciNet  Google Scholar 

  • Wang, L., Zhang, C., Tripathi, Y. M., Dey, S., & Wu, S.-J. (2021). Reliability analysis of weibull multicomponent system with stress-dependent parameters from accelerated life data. Quality and Reliability Engineering International, 37(6), 2603–2621.

    Article  Google Scholar 

  • Wiener, N. (1961). Cybernetics or control and communication in the animal and the machine. New York-London: The Massachusetts Institute of Technology Press and John Wiley & Sons. Inc.

Download references

Acknowledgements

We sincerely thank the anonymous reviewers for their constructive comments and suggestions, which have decisively contributed to improving the manuscript.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to E. I. Abdul Sathar.

Ethics declarations

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nair, R.S., Sathar, E.I.A. Bivariate dynamic weighted cumulative residual entropy. Jpn J Stat Data Sci 7, 83–100 (2024). https://doi.org/10.1007/s42081-023-00232-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s42081-023-00232-z

Keywords

Navigation