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International Conference on Information Technology and Applied Mathematics

ICITAM 2019: Recent Advances in Intelligent Information Systems and Applied Mathematics pp 209–217Cite as

On Partial Monotonic Behaviour of Past Entropy and Convolution of Extropy

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Part of the book series: Studies in Computational Intelligence ((SCI,volume 863))

Abstract

Shannon [20] gave a measure of uncertainty that plays an irresistable role in the field of communication theory. Since the proposal of the Shannon entropy many entropies have been proposed later and found to be useful in different areas. Recently, Frank et al. [6] gave a complementary dual of the Shannon entropy and named it ‘extropy’. The uncertainty associated with a random experiment is expected to get reduced when the interval containing the outcome gets smaller. However this result is in general not true for entropies with absolutely continuous random variables. In the present paper we define conditional cumulative past entropy and give the conditions necessary for its partial monotonic behaviour. Further, a result on convolution of extropy have been presented.

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Author information

Authors and Affiliations

  1. Indian Institute of Technology Kharagpur, Kharagpur, 721302, West Bengal, India

    Shilpa Bansal & Nitin Gupta

Authors
  1. Shilpa Bansal
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  2. Nitin Gupta
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Corresponding author

Correspondence to Shilpa Bansal .

Editor information

Editors and Affiliations

  1. Division of Graduate Studies and Research, Tijuana Institute of Technology, Tijuana, Mexico

    Oscar Castillo

  2. Haldia Institute of Technology, Haldia, West Bengal, India

    Dipak Kumar Jana

  3. Maulana Abul Kalam Azad University of Technology, Haringhata, India

    Debasis Giri

  4. Haldia Institute of Technology, Haldia, India

    Arif Ahmed

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Bansal, S., Gupta, N. (2020). On Partial Monotonic Behaviour of Past Entropy and Convolution of Extropy. In: Castillo, O., Jana, D., Giri, D., Ahmed, A. (eds) Recent Advances in Intelligent Information Systems and Applied Mathematics. ICITAM 2019. Studies in Computational Intelligence, vol 863. Springer, Cham. https://doi.org/10.1007/978-3-030-34152-7_16

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