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Inference on the Weibull distribution based on record values

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  • Wang, Bing Xing
  • Ye, Zhi-Sheng

Abstract

Record data are commonly seen in everyday life, e.g., concentration of emerging contaminants in environmental studies. Based on record data, this study investigates point estimation and confidence intervals estimation for the Weibull distribution. The uniformly minimum variance unbiased estimator for the Weibull shape is derived. Based on this estimator, a bias-corrected estimator for the Weibull scale is obtained and it is shown to have much smaller bias and mean squared error compared with the maximum likelihood estimator. Confidence intervals for parameters and reliability characteristics of interest are constructed using pivotal or generalized pivotal quantities. Then the results are extended to the stress–strength model involving two Weibull populations with different parameter values. Construction of confidence intervals for the stress–strength reliability is discussed under both equal shape and unequal shape scenarios. Extensive simulations are used to demonstrate the performance of confidence intervals constructed using generalized pivotal quantities.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:83:y:2015:i:c:p:26-36
    DOI: 10.1016/j.csda.2014.09.005
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    References listed on IDEAS

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    1. Sultan, K.S. & AL-Dayian, G.R. & Mohammad, H.H., 2008. "Estimation and prediction from gamma distribution based on record values," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1430-1440, January.
    2. Baklizi, Ayman, 2008. "Likelihood and Bayesian estimation of using lower record values from the generalized exponential distribution," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3468-3473, March.
    3. Stuart G. Coles & Jonathan A. Tawn, 1996. "A Bayesian Analysis of Extreme Rainfall Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 45(4), pages 463-478, December.
    4. Soliman, Ahmed A. & Abd Ellah, A.H. & Sultan, K.S., 2006. "Comparison of estimates using record statistics from Weibull model: Bayesian and non-Bayesian approaches," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 2065-2077, December.
    5. Lee, Hsiu-Mei & Lee, Wen-Chuan & Lei, Chia-Ling & Wu, Jong-Wuu, 2011. "Computational procedure of assessing lifetime performance index of Weibull lifetime products with the upper record values," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(6), pages 1177-1189.
    6. Soliman, Ahmed A. & Al-Aboud, Fahad M., 2008. "Bayesian inference using record values from Rayleigh model with application," European Journal of Operational Research, Elsevier, vol. 185(2), pages 659-672, March.
    7. Debasis Kundu & Rameshwar D. Gupta, 2005. "Estimation of P[Y > X] for generalized exponential distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 61(3), pages 291-308, June.
    8. Balakrishnan, N. & Chan, P. S., 1998. "On the normal record values and associated inference," Statistics & Probability Letters, Elsevier, vol. 39(1), pages 73-80, July.
    9. Jong-Wuu Wu & Hsiao-Chiao Tseng, 2007. "Statistical inference about the shape parameter of the Weibull distribution by upper record values," Statistical Papers, Springer, vol. 48(1), pages 95-129, January.
    10. Chan, Ping Shing, 1998. "Interval estimation of location and scale parameters based on record values," Statistics & Probability Letters, Elsevier, vol. 37(1), pages 49-58, January.
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    1. 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.
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    4. Wang, Bing Xing & Yu, Keming & Coolen, Frank P.A., 2015. "Interval estimation for proportional reversed hazard family based on lower record values," Statistics & Probability Letters, Elsevier, vol. 98(C), pages 115-122.

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