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A Goodness-of-Fit Test for the Birnbaum-Saunders Distribution Based on the Probability Plot

In: Reliability Analysis and Maintenance Optimization of Complex Systems

Author

Listed:
  • Chanseok Park

    (Pusan National University Busan)

  • Min Wang

    (The University of Texas at San Antonio)

Abstract

In the present paper, we develop a new goodness-of-fit test for the Birnbaum-Saunders distribution based on the probability plot. We utilize the sample correlation coefficient from the Birnbaum-Saunders probability plot as a measure of goodness of fit. Unfortunately, it is impossible or extremely difficult to obtain an explicit distribution of this sample correlation coefficient. To address this challenge, we employ extensive Monte Carlo simulations to obtain the empirical distribution of the sample correlation coefficient from the Birnbaum-Saunders probability plot. This empirical distribution allows us to determine the critical values alongside their corresponding significance levels, thus facilitating the computation of the $$p$$ p -value when the sample correlation coefficient is obtained. Finally, two real-data examples are provided for illustrative purposes.

Suggested Citation

  • Chanseok Park & Min Wang, 2025. "A Goodness-of-Fit Test for the Birnbaum-Saunders Distribution Based on the Probability Plot," Springer Series in Reliability Engineering, in: Qian Qian Zhao & Il Han Chung & Junjun Zheng & Jongwoon Kim (ed.), Reliability Analysis and Maintenance Optimization of Complex Systems, pages 345-359, Springer.
    • Handle: RePEc:spr:ssrchp:978-3-031-70288-4_19
    DOI: 10.1007/978-3-031-70288-4_19
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