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Interval Estimation of Generalized Inverted Exponential Distribution under Records Data: A Comparison Perspective

Author

Listed:
  • Liang Wang

    (School of Mathematics, Yunnan Normal University, Kunming 650500, China)

  • Huizhong Lin

    (School of Mathematics, Yunnan Normal University, Kunming 650500, China)

  • Yuhlong Lio

    (Department of Mathematical Sciences, University of South Dakota, Vermillion, SD 57069, USA)

  • Yogesh Mani Tripathi

    (Department of Mathematics, Indian Institute of Technology Patna, Bihta 801106, India)

Abstract

In this paper, the problem of interval estimation is considered for the parameters of the generalized inverted exponential distribution. Based on upper record values, different pivotal quantities are proposed and the associated exact and generalized confidence intervals are constructed for the unknown model parameters and reliability indices, respectively. For comparison purposes, conventional likelihood based approximate confidence intervals are also provided by using observed Fisher information matrix. Moreover, prediction intervals are also constructed for future records based on proposed pivotal quantities and likelihood procedures as well. Finally, numerical studies are carried out to investigate and compare the performances of the proposed methods and a real data analysis is presented for illustrative purposes.

Suggested Citation

  • Liang Wang & Huizhong Lin & Yuhlong Lio & Yogesh Mani Tripathi, 2022. "Interval Estimation of Generalized Inverted Exponential Distribution under Records Data: A Comparison Perspective," Mathematics, MDPI, vol. 10(7), pages 1-20, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1047-:d:778764
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    References listed on IDEAS

    as
    1. Wang, Bing Xing & Ye, Zhi-Sheng, 2015. "Inference on the Weibull distribution based on record values," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 26-36.
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    4. Wu, Shu-Fei, 2008. "Interval estimation for a Pareto distribution based on a doubly type II censored sample," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3779-3788, March.
    5. Sukhdev Singh & Yogesh Mani Tripathi & Shuo-Jye Wu, 2017. "Bayesian estimation and prediction based on lognormal record values," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(5), pages 916-940, April.
    6. Fernández, Arturo J., 2013. "Smallest Pareto confidence regions and applications," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 11-25.
    7. Dey, Sanku & Dey, Tanujit & Luckett, Daniel J., 2016. "Statistical inference for the generalized inverted exponential distribution based on upper record values," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 120(C), pages 64-78.
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