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

Mohammad Z. Raqab (), Omar M. Bdair () and Fahad M. Al-Aboud ()
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Mohammad Z. Raqab: The University of Jordan
Omar M. Bdair: Al-Balqa Applied University
Fahad M. Al-Aboud: King Abdulaziz University

Metrika: International Journal for Theoretical and Applied Statistics, 2018, vol. 81, issue 3, No 1, 229-253

Abstract: 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.

Keywords: Bayesian estimation and prediction; Gibbs and Metropolis sampling; Importance sampling; Maximum likelihood estimation; Records; Two-parameter bathtub-shaped distribution; 62F10; 62F15; 62F25; 62E25 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s00184-017-0641-0

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