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Estimating the Parameters of the Two-Parameter Rayleigh Distribution Based on Adaptive Type II Progressive Hybrid Censored Data with Competing Risks

Author

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  • Shuhan Liu

    (Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China)

  • Wenhao Gui

    (Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China)

Abstract

This paper attempts to estimate the parameters for the two-parameter Rayleigh distribution based on adaptive Type II progressive hybrid censored data with competing risks. Firstly, the maximum likelihood function and the maximum likelihood estimators are derived before the existence and uniqueness of the latter are proven. Further, Bayesian estimators are considered under symmetric and asymmetric loss functions, that is the squared error loss function, the LINEXloss function, and the general entropy loss function. As the Bayesian estimators cannot be obtained explicitly, the Lindley method is applied to compute the approximate Bayesian estimates. Finally, a simulation study is conducted, and a real dataset is analyzed for illustrative purposes.

Suggested Citation

  • Shuhan Liu & Wenhao Gui, 2020. "Estimating the Parameters of the Two-Parameter Rayleigh Distribution Based on Adaptive Type II Progressive Hybrid Censored Data with Competing Risks," Mathematics, MDPI, vol. 8(10), pages 1-16, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1783-:d:428346
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    References listed on IDEAS

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    1. Hon Keung Tony Ng & Debasis Kundu & Ping Shing Chan, 2009. "Statistical analysis of exponential lifetimes under an adaptive Type‐II progressive censoring scheme," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(8), pages 687-698, December.
    2. Howlader, Hatem A. & Hossain, Anwar M., 2002. "Bayesian survival estimation of Pareto distribution of the second kind based on failure-censored data," Computational Statistics & Data Analysis, Elsevier, vol. 38(3), pages 301-314, January.
    3. Jung-In Seo & Jae-Woo Jeon & Suk-Bok Kang, 2016. "Exact Interval Inference for the Two-Parameter Rayleigh Distribution Based on the Upper Record Values," Journal of Probability and Statistics, Hindawi, vol. 2016, pages 1-5, December.
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    Cited by:

    1. Alexey Kudryavtsev & Oleg Shestakov, 2023. "Limit Distributions for the Estimates of the Digamma Distribution Parameters Constructed from a Random Size Sample," Mathematics, MDPI, vol. 11(8), pages 1-13, April.

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