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Statistical Inference on the Shape Parameter of Inverse Generalized Weibull Distribution

Author

Listed:
  • Yan Zhuang

    (Department of Mathematics and Statistics, Connecticut College, New London, CT 06320, USA)

  • Sudeep R. Bapat

    (Shailesh J. Mehta School of Management, Indian Institute of Technology Bombay, Mumbai 400076, India)

  • Wenjie Wang

    (Department of Mathematics and Statistics, Connecticut College, New London, CT 06320, USA)

Abstract

In this paper, we propose statistical inference methodologies for estimating the shape parameter α of inverse generalized Weibull (IGW) distribution. Specifically, we develop two approaches: (1) a bounded-risk point estimation strategy for α and (2) a fixed-accuracy confidence interval estimation method for α . For (1), we introduce a purely sequential estimation strategy, which is theoretically shown to possess desirable first-order efficiency properties. For (2), we present a method that allows for the precise determination of sample size without requiring prior knowledge of the other two parameters of the IGW distribution. To validate the proposed methods, we conduct extensive simulation studies that demonstrate their effectiveness and consistency with the theoretical results. Additionally, real-world data applications are provided to further illustrate the practical applicability of the proposed procedures.

Suggested Citation

  • Yan Zhuang & Sudeep R. Bapat & Wenjie Wang, 2024. "Statistical Inference on the Shape Parameter of Inverse Generalized Weibull Distribution," Mathematics, MDPI, vol. 12(24), pages 1-16, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:24:p:3906-:d:1541546
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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. Ajit Chaturvedi & Sudeep R. Bapat & Neeraj Joshi, 2022. "Sequential Estimation of an Inverse Gaussian Mean with Known Coefficient of Variation," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 402-420, May.
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