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Estimation of the Renyi’s residual entropy of order $$\alpha $$ with dependent data

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  • R. Maya
  • E. Abdul-Sathar
  • G. Rajesh
  • K. Muraleedharan Nair

Abstract

In the present paper, we propose nonparametric estimators for the Renyi’s information measure for the residual lifetime distribution based on complete and censored data. This measure plays important roles in reliability and survival analysis in connection with modeling and analysis of life time data. Asymptotic properties of the estimators are established under suitable regularity conditions. Monte-Carlo simulation studies are carried out to compare the performance of the estimators using the mean-squared error. The methods are illustrated using real data sets. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • R. Maya & E. Abdul-Sathar & G. Rajesh & K. Muraleedharan Nair, 2014. "Estimation of the Renyi’s residual entropy of order $$\alpha $$ with dependent data," Statistical Papers, Springer, vol. 55(3), pages 585-602, August.
    • Handle: RePEc:spr:stpapr:v:55:y:2014:i:3:p:585-602
    DOI: 10.1007/s00362-013-0506-1
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    1. Cai, Zongwu & Roussas, George G., 1992. "Uniform strong estimation under [alpha]-mixing, with rates," Statistics & Probability Letters, Elsevier, vol. 15(1), pages 47-55, September.
    2. Asadi, Majid & Ebrahimi, Nader, 2000. "Residual entropy and its characterizations in terms of hazard function and mean residual life function," Statistics & Probability Letters, Elsevier, vol. 49(3), pages 263-269, September.
    3. Cai, Zongwu, 1998. "Kernel Density and Hazard Rate Estimation for Censored Dependent Data," Journal of Multivariate Analysis, Elsevier, vol. 67(1), pages 23-34, October.
    4. Felix Belzunce & Jorge Navarro & José M. Ruiz & Yolanda del Aguila, 2004. "Some results on residual entropy function," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 59(2), pages 147-161, May.
    5. Asadi, Majid & Ebrahimi, Nader & Soofi, Ehsan S., 2005. "Dynamic generalized information measures," Statistics & Probability Letters, Elsevier, vol. 71(1), pages 85-98, January.
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    Cited by:

    1. Jafar Ahmadi, 2021. "Characterization of continuous symmetric distributions using information measures of records," Statistical Papers, Springer, vol. 62(6), pages 2603-2626, December.

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