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

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  • Shu-Fei Wu

    (Department of Statistics, Tamkang University, Tamsui District, New Taipei City 251301, Taiwan)

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.

Suggested Citation

  • Shu-Fei Wu, 2024. "Interval Estimation for the Two-Parameter Exponential Distribution Based on Upper Record Value Data Using Bayesian Approaches," Mathematics, MDPI, vol. 12(23), pages 1-11, December.
  • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3868-:d:1539845
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    References listed on IDEAS

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    1. Barde, Sylvain, 2024. "Bayesian estimation of large-scale simulation models with Gaussian process regression surrogates," Computational Statistics & Data Analysis, Elsevier, vol. 196(C).
    2. Essam Al-Hussaini & Abd Ahmad, 2003. "On Bayesian interval prediction of future records," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(1), pages 79-99, June.
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