Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Bayesian Estimators Using Record Statistics of Exponentiated Inverse Weibull Distribution

  • Received : 2012.03.07
  • Accepted : 2012.04.24
  • Published : 2012.05.31
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Abstract

The inverse Weibull distribution(IWD) is a complementary Weibull distribution and plays an important role in many application areas. In this paper, we develop a Bayesian estimator in the context of record statistics values from the exponentiated inverse Weibull distribution(EIWD). We obtained Bayesian estimators through the squared error loss function (quadratic loss) and LINEX loss function. This is done with respect to the conjugate priors for shape and scale parameters. The results may be of interest especially when only record values are stored.

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References

  1. Ali, M., Pal, M. and Woo, J. (2007). Some exponentiated distributions, The Korean Communications in Statistics, 14, 93-109. https://doi.org/10.5351/CKSS.2007.14.1.093
  2. Balakrishnan, N., Ahsanullah, M. and Chan, P. S. (1992). Relations for single and product moments of record values from Gumbel distribution, Statistical and Probability Letters, 15, 223-227. https://doi.org/10.1016/0167-7152(92)90193-9
  3. Calabria, R. and Pulcini, G. (1994). Bayes 2-sample prediction for the inverse Weibull distribution, Communications in Statistics - Theory and Methods, 23, 1811-1824. https://doi.org/10.1080/03610929408831356
  4. Chandler, K. N. (1952). The distribution and frequency of record values, Journal of the Royal Statistical Society, Series B, 14, 220-228.
  5. Dumonceaux, R. and Antle, C. E. (1973). Discrimination between the lognormal and Weibull distribution, Technometrics, 15, 923-926. https://doi.org/10.1080/00401706.1973.10489124
  6. Mahmoud, M. A. W., Sultan, K. S. and Amer, S. M. (2003). Order statistics from inverse Weibull distribution and associated inference, Computational Statistics & Data Analysis, 42, 149-163. https://doi.org/10.1016/S0167-9473(02)00151-2
  7. Maswadah, M. (2003). Conditional confidence interval estimation for the inverseWeibull distribution based on censored generalized order statistics, Journal of statistical Computation and Simulation, 73, 887-898. https://doi.org/10.1080/0094965031000099140
  8. Nelson, W. B. (1982). Applied Life Data Analysis, John Willey & Sons, New York.
  9. Soland, R. M. (1969). Bayesian analysis of Weibull process with unknown scale and shape parameters, IEEE Transaction on Reliability, 18, 181-184. https://doi.org/10.1109/TR.1969.5216348
  10. Soliman, A. A., Abd Ellah, A. H. and Sultan, K. S. (2006). Comparison of estimates using record statistics fromWeibull model: Bayesian and non-Bayesian approaches, Computational Statistics & Data Analysis, 51, 2065-2077. https://doi.org/10.1016/j.csda.2005.12.020
  11. Sultan, K. S. (2008). Bayesian estimates based on record values from the inverse Weibull lifetime model, Quality Technology & Quantitative Management, 5, 363-374. https://doi.org/10.1080/16843703.2008.11673408
  12. Thompson, R. D. and Basu, A. P. (1996). Asymmetric loss function for estimating system reliability, In Bayesian Analysis in Statistics and Econometrics, edited by Berry, D. A., Chaloner, K. M., and Geweke, J. K., Willey, 471-482.
  13. Varian, H. R. (1975). A Bayesian approach to real estate assessment, In Studies in Bayesian Econometrics and Statistics in Honor of Leonard J. Savage, edited by S. E. Feinberg and A. Zellner, North Holland, Amsterdam, 195-208.
  14. Zellner, A. (1986). Bayesian estimation and prediction using asymmetric loss function, Journal of American Statistical Association, 81, 446-451. https://doi.org/10.1080/01621459.1986.10478289

Cited by

  1. Nonparametric Bayesian estimation on the exponentiated inverse Weibull distribution with record values vol.25, pp.3, 2014, https://doi.org/10.7465/jkdi.2014.25.3.611