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Inference for the two-parameter bathtub-shaped distribution based on record data

Author

Listed:
  • Mohammad Z. Raqab

    (The University of Jordan
    King Abdulaziz University)

  • Omar M. Bdair

    (Al-Balqa Applied University)

  • Fahad M. Al-Aboud

    (King Abdulaziz University)

Abstract

Here we consider the record data from the two-parameter of bathtub-shaped distribution. First, we develop simplified forms for the single moments, variances and covariance of records. These distributional properties are quite useful in obtaining the best linear unbiased estimators of the location and scale parameters which can be included in the model. The estimation of the unknown shape parameters and prediction of the future unobserved records based on some observed ones are discussed. Frequentist and Bayesian analyses are adopted for conducting the estimation and prediction problems. The likelihood method, moment based method, bootstrap methods as well as the Bayesian sampling techniques are applied for the inference problems. The point predictors and credible intervals of future record values based on an informative set of records can be developed. Monte Carlo simulations are performed to compare the so developed methods and one real data set is analyzed for illustrative purposes.

Suggested Citation

  • Mohammad Z. Raqab & Omar M. Bdair & Fahad M. Al-Aboud, 2018. "Inference for the two-parameter bathtub-shaped distribution based on record data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(3), pages 229-253, April.
    • Handle: RePEc:spr:metrik:v:81:y:2018:i:3:d:10.1007_s00184-017-0641-0
    DOI: 10.1007/s00184-017-0641-0
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    References listed on IDEAS

    as
    1. Shuo-Jye Wu, 2008. "Estimation of the two-parameter bathtub-shaped lifetime distribution with progressive censoring," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(10), pages 1139-1150.
    2. Manoj Kumar Rastogi & Yogesh Mani Tripathi & Shuo-Jye Wu, 2012. "Estimating the parameters of a bathtub-shaped distribution under progressive type-II censoring," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(11), pages 2389-2411, July.
    3. Chen, Zhenmin, 2000. "A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function," Statistics & Probability Letters, Elsevier, vol. 49(2), pages 155-161, August.
    4. Essam A. Ahmed, 2014. "Bayesian estimation based on progressive Type-II censoring from two-parameter bathtub-shaped lifetime model: an Markov chain Monte Carlo approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(4), pages 752-768, April.
    5. Shirin Shoaee & Esmaile Khorram, 2015. "Stress-Strength Reliability of a Two-Parameter Bathtub-shaped Lifetime Distribution Based on Progressively Censored Samples," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(24), pages 5306-5328, December.
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    Cited by:

    1. Ayush Tripathi & Umesh Singh & Sanjay Kumar Singh, 2021. "Inferences for the DUS-Exponential Distribution Based on Upper Record Values," Annals of Data Science, Springer, vol. 8(2), pages 387-403, June.
    2. Siyi Chen & Wenhao Gui, 2020. "Statistical Analysis of a Lifetime Distribution with a Bathtub-Shaped Failure Rate Function under Adaptive Progressive Type-II Censoring," Mathematics, MDPI, vol. 8(5), pages 1-21, April.
    3. A. Asgharzadeh & S. F. Bagheri & N. A. Ibrahim & M. R. Abubakar, 2020. "Optimal confidence regions for the two-parameter exponential distribution based on records," Computational Statistics, Springer, vol. 35(1), pages 309-326, March.
    4. Zihui Zhang & Wenhao Gui, 2022. "Statistical Analysis of the Lifetime Distribution with Bathtub-Shaped Hazard Function under Lagged-Effect Step-Stress Model," Mathematics, MDPI, vol. 10(5), pages 1-23, February.
    5. Abu Awwad Raed R. & Bdair Omar M. & Abufoudeh Ghassan K., 2021. "Bayesian estimation and prediction based on Rayleigh record data with applications," Statistics in Transition New Series, Statistics Poland, vol. 22(3), pages 59-79, September.
    6. Raed R. Abu Awwad & Omar M. Bdair & Ghassan K. Abufoudeh, 2021. "Bayesian estimation and prediction based on Rayleigh record data with applications," Statistics in Transition New Series, Polish Statistical Association, vol. 22(3), pages 59-79, September.

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