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On empirical cumulative residual entropy and a goodness-of-fit test for exponentiality

Author

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  • V. Zardasht
  • S. Parsi
  • M. Mousazadeh

Abstract

The cumulative residual entropy (CRE) is a new measure of information and an alternative to the Shannon differential entropy in which the density function is replaced by the survival function. This new measure overcomes deficiencies of the differential entropy while extending the Shannon entropy from the discrete random variable cases to the continuous counterpart. Some properties of the cumulative residual entropy, its estimation and applications has been studied by many researchers. The objective of this paper is twofold. In the first part, we give a central limit theorem result for the empirical cumulative residual entropy based on a right censored random sample from an unknown distribution. In the second part, we use the CRE of the comparison distribution function to propose a goodness-of-fit test for the exponential distribution. The performance of the test statistic is evaluated using a simulation study. Finally, some numerical examples illustrating the theory are also given. Copyright The Author(s) 2015

Suggested Citation

  • V. Zardasht & S. Parsi & M. Mousazadeh, 2015. "On empirical cumulative residual entropy and a goodness-of-fit test for exponentiality," Statistical Papers, Springer, vol. 56(3), pages 677-688, August.
    • Handle: RePEc:spr:stpapr:v:56:y:2015:i:3:p:677-688
    DOI: 10.1007/s00362-014-0603-9
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    Citations

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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.
    2. Benchong Li & Liya Fu, 2018. "Exact test of goodness of fit for binomial distribution," Statistical Papers, Springer, vol. 59(3), pages 851-860, September.
    3. Asok K. Nanda & Shovan Chowdhury, 2021. "Shannon's Entropy and Its Generalisations Towards Statistical Inference in Last Seven Decades," International Statistical Review, International Statistical Institute, vol. 89(1), pages 167-185, April.
    4. Marius Giuclea & Costin-Ciprian Popescu, 2022. "On Geometric Mean and Cumulative Residual Entropy for Two Random Variables with Lindley Type Distribution," Mathematics, MDPI, vol. 10(9), pages 1-10, April.
    5. Amit Ghosh & Chanchal Kundu, 2019. "Bivariate extension of (dynamic) cumulative residual and past inaccuracy measures," Statistical Papers, Springer, vol. 60(6), pages 2225-2252, December.
    6. G. Rajesh & S. M. Sunoj, 2019. "Some properties of cumulative Tsallis entropy of order $$\alpha $$ α," Statistical Papers, Springer, vol. 60(3), pages 933-943, June.
    7. Mohamed Said Mohamed, 2020. "On Cumulative Tsallis Entropy and Its Dynamic Past Version," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(4), pages 1903-1917, December.
    8. J. S. Allison & L. Santana & N. Smit & I. J. H. Visagie, 2017. "An ‘apples to apples’ comparison of various tests for exponentiality," Computational Statistics, Springer, vol. 32(4), pages 1241-1283, December.
    9. Klein, Ingo & Mangold, Benedikt, 2015. "Cumulative Paired 𝜙-Entropy," FAU Discussion Papers in Economics 07/2015, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.

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