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Parameter Estimation of Exponentiated Half-Logistic Distribution for Left-Truncated and Right-Censored Data

Author

Listed:
  • Xifan Song

    (School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, China)

  • Ziyu Xiong

    (School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, China)

  • Wenhao Gui

    (School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, China)

Abstract

Left-truncated and right-censored data are widely used in lifetime experiments, biomedicine, labor economics, and actuarial science. This article discusses how to resolve the problems of statistical inferences on the unknown parameters of the exponentiated half-logistic distribution based on left-truncated and right-censored data. In the beginning, maximum likelihood estimations are calculated. Then, asymptotic confidence intervals are constructed by using the observed Fisher information matrix. To cope with the small sample size scenario, we employ the percentile bootstrap method and the bootstrap-t method for the establishment of confidence intervals. In addition, Bayesian estimations under both symmetric and asymmetric loss functions are addressed. Point estimates are computed by Tierney–Kadane’s approximation and importance sampling procedure, which is also applied to establishing corresponding highest posterior density credible intervals. Lastly, simulated and real data sets are presented and analyzed to show the effectiveness of the proposed methods.

Suggested Citation

  • Xifan Song & Ziyu Xiong & Wenhao Gui, 2022. "Parameter Estimation of Exponentiated Half-Logistic Distribution for Left-Truncated and Right-Censored Data," Mathematics, MDPI, vol. 10(20), pages 1-26, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3838-:d:944824
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    References listed on IDEAS

    as
    1. Balakrishnan, N. & Mitra, Debanjan, 2012. "Left truncated and right censored Weibull data and likelihood inference with an illustration," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4011-4025.
    2. Kundu, Debasis & Mitra, Debanjan, 2016. "Bayesian inference of Weibull distribution based on left truncated and right censored data," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 38-50.
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