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A goodness-of-fit test for testing exponentiality based on normalized dynamic survival extropy

  • Gaurav Kandpal EMAIL logo and Nitin Gupta
Published/Copyright: June 9, 2025
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Abstract

An updated version of the cumulative residual extropy (CRJ) with some dynamic features is introduced in this study as normalized dynamic survival extropy (NDSE). We observe that NDSE grabs attention in the reliability theory also, since NDSE of the relevant random variable in the age replacement model is always equal to the CRJ of that variable. This paper proposes an NDSE based non-parametric test that can be used to see if a data set follows an exponential trend. The proposed test makes itself unique due to its exact distribution of test statistics, scale invariant property, consistency, asymptotic normality, great power and simplicity in calculation. Being aware of the problem of censored observation, we explained how our test will be applied to it. We also provide an extensive power comparison with 5 different tests, each taking different alternatives, and a few real-life examples.


Gaurav Kandpal would like to acknowledge financial support from the University Grant Commission, Government of India (Student ID: 221610071232).


Acknowledgement

The authors are thankful to reviewers for carefully checking the mathematical accuracy of the manuscript.

  1. (Communicated by Gejza Wimmer)

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Received: 2024-10-01
Accepted: 2024-12-24
Published Online: 2025-06-09
Published in Print: 2025-06-26

© 2025 Mathematical Institute Slovak Academy of Sciences

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