Interval Estimation for the Two-Parameter Exponential Distribution Based on Upper Record Value Data Using Bayesian Approaches

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Title:	Interval Estimation for the Two-Parameter Exponential Distribution Based on Upper Record Value Data Using Bayesian Approaches
Authors:	Wu, Shu-fei
Keywords:	upper record value;two-parameter exponential distribution;Bayesian credible interval estimation;Bayesian credible confidence region;Bayesian prediction interval
Date:	2024-12-09
Issue Date:	2025-03-20 09:31:21 (UTC+8)
Publisher:	MDPI
Abstract:	Using upper record value data, we provide a credible interval estimate for the scale parameter of a two-parameter exponential distribution based on Bayesian methods. Additionally, we propose two Bayesian credible confidence regions for both parameters. In addition to interval estimations for the parameters, we propose a Bayesian prediction interval for a future upper record value. A simulation study is conducted to compare the performance of the proposed Bayesian credible interval, regions and prediction intervals with existing non-Bayesian approaches, focusing on coverage probabilities. The simulation results show that the Bayesian approaches achieve higher coverage probabilities than existing methods. Finally, we use an engineering example to demonstrate all the proposed Bayesian credible estimations for the exponential distribution based on upper record value data.
Relation:	Mathematics 12(23),　3868
DOI:	10.3390/math12233868
Appears in Collections:	[Graduate Institute & Department of Statistics] Journal Article

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