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Non-Parametric Test for Decreasing Uncertainty of Residual Life Distribution (DURL)

Author

Listed:
  • Hassina Benaoudia

    (Department of Probability and Statistics, Faculty of Mathematics, University of Science and Technology Houari Boumedienne, Bab Ezzouar, Algiers 16111, Algeria
    These authors contributed equally to this work.)

  • Amar Aissani

    (Laboratory of Research in Intelligent Informatics, Mathematics and Applications (RIIMA), Faculty of Computer Science, University of Science and Technology Houari Boumedienne, Bab Ezzouar, Algiers 16111, Algeria
    These authors contributed equally to this work.)

Abstract

In this paper, we propose a new statistic to test the monotonicity of uncertainty based on derivative criteria and the histogram method. We test the null hypothesis that residual entropy is constant against the fact that it decreases over time. Hence, by the fact that the exponential distribution is the distribution with a constant uncertainty, we establish the test exponential distribution against the decreasing uncertainty of residual life distribution. Consistency and asymptotic normality are proved. The critical values of the statistics are given by means of the Monte Carlo simulation method to decide on the test. Then, the power estimates of the new test are compared to those of the test based on the criteria of monotonicity of residual entropy. Finally, we show, with real survival data, that the distributions belong to a decreasing uncertainty residual life class. Moreover, by applying a test of goodness of fit, we confirm that the data follow parametric distributions belonging to a decreasing uncertainty of residual life class.

Suggested Citation

  • Hassina Benaoudia & Amar Aissani, 2023. "Non-Parametric Test for Decreasing Uncertainty of Residual Life Distribution (DURL)," Mathematics, MDPI, vol. 11(20), pages 1-17, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4227-:d:1256517
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    References listed on IDEAS

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    1. 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.
    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. Mark Colyvan, 2008. "Is Probability the Only Coherent Approach to Uncertainty?," Risk Analysis, John Wiley & Sons, vol. 28(3), pages 645-652, June.
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