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Estimation of δ= P ( X > Y ) for Burr XII distribution based on the progressively first failure-censored samples

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  • Y. L. Lio
  • Tzong-Ru Tsai

Abstract

Let X and Y have two-parameter Burr XII distributions. The maximum-likelihood estimator of δ= P ( X > Y ) is studied under the progressively first failure-censored samples. Three confidence intervals of δ are constructed by using an asymptotic distribution of the maximum-likelihood estimator of δ and two bootstrapping procedures, respectively. Some computational results from intensive simulations are presented. An illustrative example is provided to demonstrate the application of the proposed method.

Suggested Citation

  • Y. L. Lio & Tzong-Ru Tsai, 2012. "Estimation of δ= P ( X > Y ) for Burr XII distribution based on the progressively first failure-censored samples," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(2), pages 309-322, April.
    • Handle: RePEc:taf:japsta:v:39:y:2012:i:2:p:309-322
    DOI: 10.1080/02664763.2011.586684
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    References listed on IDEAS

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    1. Wu, Shuo-Jye & Kus, Coskun, 2009. "On estimation based on progressive first-failure-censored sampling," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3659-3670, August.
    2. Chansoo Kim & Younshik Chung, 2006. "Bayesian estimation of P (Y>X) from Burr-type X model containing spurious observations," Statistical Papers, Springer, vol. 47(4), pages 643-651, October.
    3. Dallas Wingo, 1993. "Maximum likelihood methods for fitting the burr type XII distribution to multiply (progressively) censored life test data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 40(1), pages 203-210, December.
    4. 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.
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    Cited by:

    1. Shubham Saini & Renu Garg, 2022. "Reliability inference for multicomponent stress–strength model from Kumaraswamy-G family of distributions based on progressively first failure censored samples," Computational Statistics, Springer, vol. 37(4), pages 1795-1837, September.
    2. Ehsan Fayyazishishavan & Serpil Kılıç Depren, 2021. "Inference of stress-strength reliability for two-parameter of exponentiated Gumbel distribution based on lower record values," PLOS ONE, Public Library of Science, vol. 16(4), pages 1-12, April.
    3. Essam A. Ahmed, 2017. "Estimation and prediction for the generalized inverted exponential distribution based on progressively first-failure-censored data with application," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(9), pages 1576-1608, July.
    4. M. S. Kotb & M. Z. Raqab, 2021. "Estimation of reliability for multi-component stress–strength model based on modified Weibull distribution," Statistical Papers, Springer, vol. 62(6), pages 2763-2797, December.
    5. Jessie Marie Byrnes & Yu-Jau Lin & Tzong-Ru Tsai & Yuhlong Lio, 2019. "Bayesian Inference of δ = P ( X < Y ) for Burr Type XII Distribution Based on Progressively First Failure-Censored Samples," Mathematics, MDPI, vol. 7(9), pages 1-24, September.
    6. Filippo Domma & Sabrina Giordano, 2013. "A copula-based approach to account for dependence in stress-strength models," Statistical Papers, Springer, vol. 54(3), pages 807-826, August.
    7. Ajit Chaturvedi & Renu Garg & Shubham Saini, 2022. "Estimation and testing procedures for the reliability characteristics of Kumaraswamy-G distributions based on the progressively first failure censored samples," OPSEARCH, Springer;Operational Research Society of India, vol. 59(2), pages 494-517, June.
    8. Akram Kohansal, 2019. "On estimation of reliability in a multicomponent stress-strength model for a Kumaraswamy distribution based on progressively censored sample," Statistical Papers, Springer, vol. 60(6), pages 2185-2224, December.
    9. Yuhlong Lio & Tzong-Ru Tsai & Liang Wang & Ignacio Pascual Cecilio Tejada, 2022. "Inferences of the Multicomponent Stress–Strength Reliability for Burr XII Distributions," Mathematics, MDPI, vol. 10(14), pages 1-28, July.

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