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

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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.

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Acknowledgements

This research project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under Grant No. (22-135-35-HiCi). The authors, therefore, acknowledge with thanks DSR technical and financial support. The authors also thank the editor and referees for their comments and helpful suggestions which helped to improve the presentation.

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Authors and Affiliations

  1. Department of Mathematics, The University of Jordan, Amman, 11942, Jordan

    Mohammad Z. Raqab

  2. King Abdulaziz University, Jeddah, Saudi Arabia

    Mohammad Z. Raqab & Fahad M. Al-Aboud

  3. Faculty of Engineering Technology, Al-Balqa Applied University, Amman, 11134, Jordan

    Omar M. Bdair

Authors
  1. Mohammad Z. Raqab
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  2. Omar M. Bdair
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  3. Fahad M. Al-Aboud
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Correspondence to Mohammad Z. Raqab.

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Raqab, M.Z., Bdair, O.M. & Al-Aboud, F.M. Inference for the two-parameter bathtub-shaped distribution based on record data. Metrika 81, 229–253 (2018). https://doi.org/10.1007/s00184-017-0641-0

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