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Doubly truncated (interval) cumulative residual and past entropy

Author

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  • Khorashadizadeh, M.
  • Rezaei Roknabadi, A.H.
  • Mohtashami Borzadaran, G.R.

Abstract

Two measures of uncertainty, the cumulative residual entropy (CRE) and doubly truncated Shannon entropy have been introduced respectively by Rao et al. (2004) and Sunoj et al. (2009). In this paper we proposed the doubly truncated (interval) cumulative residual entropy (ICRE), which is an extension of CRE and the dynamic CRE defined by Asadi and Zohrevand (2007). We study some properties and characterization of this measure, including its connections with doubly truncated Shannon entropy and mean residual life. Also, the dual measure, doubly truncated (interval) cumulative past entropy (ICPE) is defined and some of its properties are studied. Furthermore, their monotonicity and associated aging classes of distributions are discussed and the upper (lower) bound for them are obtained. Finally for exponential distribution all entropies are presented.

Suggested Citation

  • Khorashadizadeh, M. & Rezaei Roknabadi, A.H. & Mohtashami Borzadaran, G.R., 2013. "Doubly truncated (interval) cumulative residual and past entropy," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1464-1471.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:5:p:1464-1471
    DOI: 10.1016/j.spl.2013.01.033
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    References listed on IDEAS

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    1. Misagh, F. & Yari, G.H., 2011. "On weighted interval entropy," Statistics & Probability Letters, Elsevier, vol. 81(2), pages 188-194, February.
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    3. Ebrahimi, Nader & Kirmani, S. N. U. A., 1996. "Some results on ordering of survival functions through uncertainty," Statistics & Probability Letters, Elsevier, vol. 29(2), pages 167-176, August.
    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. Asok Nanda & Prasanta Paul, 2006. "Some Properties of Past Entropy and their Applications," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 64(1), pages 47-61, August.
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    1. Antonio Di Crescenzo & Abdolsaeed Toomaj, 2022. "Weighted Mean Inactivity Time Function with Applications," Mathematics, MDPI, vol. 10(16), pages 1-30, August.

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