Skip to main content
Log in

Some Results on DDCRE Class of Life Distributions

  • Published:
Sankhya A Aims and scope Submit manuscript

Abstract

Asadi and Zohrevand (2007). On the dynamic cumulative residual entropy. J. Statist. Plann. Inference, 137, 1931–1941] define the decreasing dynamic cumulative residual entropy (DDCRE) class of life distributions, some properties of the DDCRE class are studied. Navarro et al. (2010). Some new results on the cumulative residual entropy. J. Statist. Plann. Inference, 140, 310–322] further investigate this class, they get some results concerning the relations between the DDCRE class and other classes of distributions. In the present paper some characterization properties of the DDCRE class are investigated, closure and reversed closure properties of this class are obtained.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Asadi M. and Ebrahimi N. (2000). Residual entropy and its characterizations in terms of hazard function and mean residual life function. Statist. Probab. Lett., 49, 263–269.

    Article  MathSciNet  MATH  Google Scholar 

  • Asadi M. and Zohrevand Y. (2007). On the dynamic cumulative residual entropy. J. Statist. Plann. Inference, 137, 1931–1941.

    Article  MathSciNet  MATH  Google Scholar 

  • Barlow R.E. and Proschan F. 1981 .Statistical Theory of Reliability and Life Testing, To Begin with, Silver Spring, Maryland.

  • Belzunce F., Navarro J., Ruiz J.M., and del Aguila Y. (2004). Some results on residual entropy function. Metrika, 59, 47–161.

    Article  Google Scholar 

  • Di Crescenzo A. and Longobardi M. (2002). Entropy-based measure of uncertainty in past lifetime distributions. J. Appl. Probab., 39, 434–440.

    Article  MathSciNet  MATH  Google Scholar 

  • Di Crescenzo A. and Longobardi M. (2006). On weighted and residual and past entropies. Scientiae Math. Japan, 64, 255–266.

    MathSciNet  MATH  Google Scholar 

  • Ebrahimi N. (1996). How to measure uncertainty in the residual lifetime distribution. Sankhyā A, 58, 48–56.

    MathSciNet  MATH  Google Scholar 

  • Ebrahimi N. and Kirmani S.N.U.A. (1996). Some results on odering of survival functions through uncertainty. Statist. Probab. Lett., 29, 167–176.

    Article  MathSciNet  MATH  Google Scholar 

  • Ebrahimi N. and Pellerey F. (1995). New partial ordering of survival functions based on the notion of uncertainty. J. Appl. Probab., 32, 202–211.

    Article  MathSciNet  MATH  Google Scholar 

  • Khorashadizadeh M., Rezaei Roknabadi A.H., and Mohtashami Borzadaran G.R. (2013). Doubly truncated (interval) cumulative residual and past entropy. Statist. Probab. Lett., 83, 1464–1471.

    Article  MathSciNet  MATH  Google Scholar 

  • Kumar V. and Taneja H.C. (2011). Some characterization results on generalized cumulative residual entropy measure. Statist. Probab. Lett., 81, 1072–1077.

    Article  MathSciNet  MATH  Google Scholar 

  • Li X. and Zhang S. (2011). Some new results on Rényi entropy of residual life and inactivity time. Prob. Eng. Inf. Sci., 25, 237–250.

    Article  MATH  Google Scholar 

  • Li X. and Zuo M.J. (2004). Preservation of stochastic orders for random minima and maxima, with applications. Naval Res. Logist., 51, 332–344.

    Article  MathSciNet  MATH  Google Scholar 

  • Navarro J., del Aguila Y., and Asadi M. (2010). Some new results on the cumulative residual entropy. J. Statist. Plann. Inference, 140, 310–322.

    Article  MathSciNet  MATH  Google Scholar 

  • Rao M., Chen Y., Vernuri B.C., and Wang F. (2004). Cumulative residual entropy: a new measure of information. IEEE Trans. Inform. Theory, 50, 1220–1228.

    Article  MathSciNet  MATH  Google Scholar 

  • Shaked M. and Shanthikumar J.G. (1994). Stochastic Orders and Their Applications. Academic Press, San Diego.

    MATH  Google Scholar 

  • Shaked M. and Shanthikumar J.G. (2007). Stochastic Orders. Springer, New York.

    Book  MATH  Google Scholar 

  • Shannon C.E. (1948). A mathematical theory of comunication. Bell Syst. Tech. J., 27, 379–423.

    Article  MathSciNet  MATH  Google Scholar 

  • Sunoj S.M. and Sankaran P.G. (2012). Quantile based entropy function. Statist. Probab. Lett., 82, 1049–1053.

    Article  MathSciNet  MATH  Google Scholar 

  • Sunoj S.M., Sankaran P.G., and Nanda A.K. (2013). Quantile based entropy function in past lifetime. Statist. Probab. Lett., 83, 366–372.

    Article  MathSciNet  MATH  Google Scholar 

  • Taneja I.J. 1990 . On Generalized Entropy with Applications. In Lectures in Applied Mathematics and Informatics, (L.M. Ricciardi, ed.). Manchester University Press, pp. 107–169.

  • Wiener N. (1961). Cybernetics, 2nd edn. MIT Press, Wiley, New York.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Dian-tong Kang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kang, Dt. Some Results on DDCRE Class of Life Distributions. Sankhya A 77, 351–363 (2015). https://doi.org/10.1007/s13171-014-0065-0

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13171-014-0065-0

Keywords and phrases

AMS (2000) subject classification

Navigation