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On cumulative residual (past) inaccuracy for truncated random variables

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Abstract

To overcome the drawbacks of Shannon’s entropy, the concept of cumulative residual and past entropy has been proposed in the information theoretic literature. Furthermore, the Shannon entropy has been generalized in a number of different ways by many researchers. One important extension is Kerridge inaccuracy measure. In the present communication we study the cumulative residual and past inaccuracy measures, which are extensions of the corresponding cumulative entropies. Several properties, including monotonicity and bounds, are obtained for left, right and doubly truncated random variables.

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Acknowledgments

We thank an anonymous referee for his/her useful comments and suggestions on the earlier version of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Rajiv Gandhi Institute of Petroleum Technology, Rae Bareli, U.P., 229 316, India

    Chanchal Kundu

  2. Dipartimento di Matematica, Università di Salerno, Via Giovanni Paolo II, n. 132, 84084, Fisciano, SA, Italy

    Antonio Di Crescenzo

  3. Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Via Cintia, 80126, Naples, Italy

    Maria Longobardi

Authors
  1. Chanchal Kundu
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  2. Antonio Di Crescenzo
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  3. Maria Longobardi
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Corresponding author

Correspondence to Chanchal Kundu.

Additional information

The work of C. Kundu is supported by Department of Science and Technology, Government of India (Ref. No. SR/FTP/MS-016/2012) and the research by A. Di Crescenzo and M. Longobardi is partially supported by GNCS-INdAM and Regione Campania (Legge 5).

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Kundu, C., Di Crescenzo, A. & Longobardi, M. On cumulative residual (past) inaccuracy for truncated random variables. Metrika 79, 335–356 (2016). https://doi.org/10.1007/s00184-015-0557-5

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  • DOI: https://doi.org/10.1007/s00184-015-0557-5

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