Statistical Inference on the Shape Parameter of Inverse Generalized Weibull Distribution

In this paper, we propose statistical inference methodologies for estimating the shape parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula...

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Bibliographic Details
Main Authors: Yan Zhuang, Sudeep R. Bapat, Wenjie Wang
Format: Article
Language:English
Published: MDPI AG 2024-12-01
Series:Mathematics
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Online Access:https://www.mdpi.com/2227-7390/12/24/3906
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Summary:In this paper, we propose statistical inference methodologies for estimating the shape parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> of inverse generalized Weibull (IGW) distribution. Specifically, we develop two approaches: (1) a bounded-risk point estimation strategy for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> and (2) a fixed-accuracy confidence interval estimation method for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>. 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.
ISSN:2227-7390