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Energy Statistic-Based Goodness-of-Fit Test for the Lindley Distribution with Application to Lifetime Data

Author

Listed:
  • Joseph Njuki

    (Department of Mathematics and Statistics, Coastal Carolina University, Conway, SC 29526, USA)

  • Ryan Avallone

    (Department of Mathematics and Statistics, Coastal Carolina University, Conway, SC 29526, USA)

Abstract

In this article, we propose a goodness-of-fit test for a one-parameter Lindley distribution based on energy statistics. The Lindley distribution has been widely used in reliability studies and survival analysis, especially in applied sciences. The proposed test procedure is simple and more powerful against general alternatives. Under different settings, Monte Carlo simulations show that the proposed test is able to be well controlled for any given nominal levels. In terms of power, the proposed test outperforms other existing similar methods in different settings. We then apply the proposed test to real-life datasets to demonstrate its competitiveness and usefulness.

Suggested Citation

  • Joseph Njuki & Ryan Avallone, 2025. "Energy Statistic-Based Goodness-of-Fit Test for the Lindley Distribution with Application to Lifetime Data," Stats, MDPI, vol. 8(4), pages 1-14, September.
    • Handle: RePEc:gam:jstats:v:8:y:2025:i:4:p:87-:d:1759402
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    References listed on IDEAS

    as
    1. M. E. Ghitany & D. K. Al-Mutairi, 2008. "Size-biased Poisson-Lindley distribution and its application," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 299-311.
    2. Rizzo, Maria L., 2009. "New Goodness-of-Fit Tests for Pareto Distributions," ASTIN Bulletin, Cambridge University Press, vol. 39(2), pages 691-715, November.
    3. Vexler, Albert & Gurevich, Gregory, 2010. "Empirical likelihood ratios applied to goodness-of-fit tests based on sample entropy," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 531-545, February.
    4. Ghitany, M.E. & Al-Mutairi, D.K. & Nadarajah, S., 2008. "Zero-truncated Poisson–Lindley distribution and its application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 279-287.
    5. David S. Matteson & Nicholas A. James, 2014. "A Nonparametric Approach for Multiple Change Point Analysis of Multivariate Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 334-345, March.
    6. Ghitany, M.E. & Atieh, B. & Nadarajah, S., 2008. "Lindley distribution and its application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 78(4), pages 493-506.
    7. Szekely, Gábor J. & Rizzo, Maria L., 2005. "A new test for multivariate normality," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 58-80, March.
    8. Wei Ning & Grace Ngunkeng, 2013. "An empirical likelihood ratio based goodness-of-fit test for skew normality," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(2), pages 209-226, June.
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