Statistical Inference on the Shape Parameter of Inverse Generalized Weibull Distribution

Yan Zhuang (), Sudeep R. Bapat and Wenjie Wang
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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

Mathematics, 2024, vol. 12, issue 24, 1-16

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.

Keywords: inverse generalized Weibull; shape parameter; estimation; sequential procedures; bladder cancer (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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