Improved Bayes estimators and prediction for the Wilson-Hilferty distribution.

In this paper, we revisit the Wilson-Hilferty distribution and presented its mathematical properties such as the r-th moments and reliability properties. The parameters estimators are discussed using objective reference Bayesian analysis for both complete and censored data where the resulting marginal posterior intervals have accurate frequentist coverage. A simulation study is presented to compare the performance of the proposed estimators with the frequentist approach where it is observed a clear advantage for the Bayesian method. Finally, the proposed methodology is illustrated on three real datasets.

[1]  Debasis Kundu,et al.  Prediction for future failures in Weibull distribution under hybrid censoring , 2015 .

[2]  James O. Berger,et al.  Overall Objective Priors , 2015, 1504.02689.

[3]  S. Nadarajah,et al.  Kumaraswamy distribution: different methods of estimation , 2018 .

[4]  D. Cox,et al.  Parameter Orthogonality and Approximate Conditional Inference , 1987 .

[5]  B. R. Crain,et al.  ASYMPTOTIC NORMALITY OF THE POSTERIOR DISTRIBUTION FOR EXPONENTIAL MODELS , 1975 .

[6]  Francisco Louzada,et al.  The Inverse Nakagami-m Distribution: A Novel Approach in Reliability , 2018, IEEE Transactions on Reliability.

[7]  Technology,et al.  On the systematic errors of cosmological-scale gravity tests using redshift-space distortion: non-linear effects and the halo bias , 2013, 1308.6087.

[8]  Creasy Problem,et al.  Reference Posterior Distributions for Bayesian Inference , 1979 .

[9]  Francisco Louzada,et al.  Posterior Properties of the Nakagami-m Distribution Using Noninformative Priors and Applications in Reliability , 2018, IEEE Transactions on Reliability.

[10]  E. Stacy.  A Generalization of the Gamma Distribution , 1962 .

[11]  E. B. Wilson,et al.  The Distribution of Chi-Square. , 1931, Proceedings of the National Academy of Sciences of the United States of America.

[12]  R. Tibshirani.  Noninformative priors for one parameter of many , 1989 .

[13]  Jorge Alberto Achcar,et al.  Bayesian analysis of the generalized gamma distribution using non-informative priors , 2017 .

[14]  S. M. Hoseini,et al.  Comparison of estimation methods for the Weibull distribution , 2013 .

[15]  Mahmoud Zemzami,et al.  Improvement of artificial neural networks to predict daily streamflow in a semi-arid area , 2016 .

[16]  Debasis Kundu,et al.  Bayesian Inference and prediction or order statistics for a Type II censored Weibull distribution , 2012 .

[17]  Debasis Kundu,et al.  Bayes estimation and prediction of the two-parameter gamma distribution , 2011 .