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Exact Interval Inference for the Two-Parameter Rayleigh Distribution Based on the Upper Record Values

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  • Jung-In Seo
  • Jae-Woo Jeon
  • Suk-Bok Kang

Abstract

The maximum likelihood method is the most widely used estimation method. On the other hand, it can produce substantial bias, and an approximate confidence interval based on the maximum likelihood estimator cannot be valid when the sample size is small. Because the sizes of the record values are considerably smaller than the original sequence observed in the majority of cases, a method appropriate for this situation is required for precise inference. This paper provides the exact confidence intervals for unknown parameters and exact predictive intervals for the future upper record values by providing some pivotal quantities in the two-parameter Rayleigh distribution based on the upper record values. Finally, the validity of the proposed inference methods was examined from Monte Carlo simulations and real data.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnljps:8246390
    DOI: 10.1155/2016/8246390
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    Cited by:

    1. 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.

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