31Dec 2016

ESTIMATION OF PARAMETERS USING LINDLEY’S METHOD.

  • Research Scholar, Department of Statistics, Loyola College, Chennai–34, India.
  • Associate Professor, Department of Statistics, Loyola College, Chennai–34, India.
Crossref Cited-by Linking logo
  • Abstract
  • Keywords
  • References
  • Cite This Article as
  • Corresponding Author

In this paper, we consider the estimation problem of the parameters of the Constant Shape Bi-Weibull Distribution based on a Failure Time data. We use the method of Maximum Likelihood and Bayesian estimation to estimate parameters. The Bayesian estimates are obtained using Lindleys approximation technique with Jeffreys Prior information and Extension of Jeffreys Prior information under three loss functions. The comparisons between different estimators are made based on simulation study and a real time data.

  1. Abdel-Wahid, A. and Winterbottom, A. (1987). Approximate Bayesian Estimates for the Weibull Reliability Function and Hazard Rate from Censored Data, J. Stat Plann and Infer, 16, 277-283.
  2. Al-Aboud, F. M. (2009). Bayesian Estimation for the Extreme Value Distribution Using Progressive Censored Data and Asymmetric Loss, International Mathematical Forum, 4, 1603-1622.
  3. Al-Athari, F. M. (2011). Parameter Estimation for the Double-Pareto Distribution, J. Math Stat, 7, 289-294.
  4. Al Omari, M. A. and Ibrahim, N. A. (2011). Bayesian Survival Estimation for Weibull Distribution with Censored Data, J. ApplSci, 11, 393-396.
  5. Calabria, R. and Pulcini, G. (1996). Point Estimation under Asymmetric Loss Function for Left Truncated Exponential Samples, Comm Stat Theor Meth, 25, 585-600.
  6. Guure, C. B., Ibrahim, N. A. and Adam, M. B. (2013). Bayesian Inference of the Weibull Model Based on Interval-Censored Survival Data. Comp Math Methods Med, Article ID 849520, 10 pages.
  7. Guure, C. B. and Ibrahim, N.A. (2012a). Bayesian analysis of the survival function and failure rate of Weibull distribution with censored data, Math ProblEng, Article ID. 329489, 18 pages.
  8. Guure, C. B., Ibrahim, N. A. and Al Omari, A. M. (2012). Bayesian Estimation of Two-Parameter Weibull Distribution using Extension of Jeffreys' Prior Information with Three Loss Functions. Math Probl Eng., Article ID. 589640. 13 pages.
  9. Lavanya, A. and Leo Alexander, T. (2016). Confidence Intervals Estimation for ROC Curve, AUC and Brier Score under the Constant Shape Bi-Weibull Distribution, International Journal of Science and Research, 5, 8, 371-378.
  10. Lavanya, A. and Leo Alexander, T. (2016). Asymmetric and Symmetric Properties of Constant Shape Bi-Weibull ROC Curve Described by Kullback-Leibler Divergences, International Journal of Applied Research, 2, 8, 713-720.
  11. Lavanya, A. and Leo Alexander, T. (2016). Bayesian Estimation of Parameters under the Constant Shape Bi-Weibull Distribution Using Extension of Jeffreys’ Prior Information with Three Loss Functions, International Journal of Science and Research, 5, 9, 96-103.
  12. Lavanya, A. and Leo Alexander, T. (2016). Bayesian Estimation of the Failure Rate Using Extension of Jeffreys Prior Information with Three Loss Functions, International Journal of Science and Research, 5, 9, 736-742.
  13. Lavanya, A. and Leo Alexander, T. (2016).Estimation Of The Survival Function Under The Constant Shape Bi-Weibull Failure Time Distribution Based On Three Loss Functions, International Journal of advanced Research, 4, 9, 1225-1234.
  14. Leo Alexander, T. and Lavanya, A. (2016). Functional Relationship between Brier Score and Area Under the Constant Shape Bi-Weibull ROC Curve, International Journal of Recent Scientific Research 7, 7, 12330-12336.
  15. Leo Alexander, T. and Lavanya, A. (2016). Estimation Of AUC For Constant Shape Bi-Weibull Failure Time Distribution, International Journal of Recent Scientific Research, 7, 10, 13826-13836.
  16. Pandey, B. N., Dwividi, N. and Pulastya, B. (2011). Comparison Between Bayesian and Maximum Likelihood Estimation of the Scale Parameter in Weibull Distribution with Known Shape Under Linex Loss Function, J. Sci Res, 55, 163-172.
  17. Sinha, S. k. and Sloan, J.A. (1988). Bayes Estimation of the Parameters and Reliability Function of the 3-Parameter Weibull Distribution, IEEE Transactions on Reliability, 37, 364-369.
  18. Sinha S. K. (1986). Bayes Estimation of the Reliability Function and Hazard Rate of a Weibull Failure Time Distribution, Tranbajos De Estadistica, 1, 47-56.
  19. Soliman, A. A., AbdEllah, A. H. and Ryan, S. B. (2006). Comparison of Estimates Using Record Statistics FromWeibull Model: Bayesian and Non-Bayesian Approaches. Comput Stat Data Anal, 51, 2065-2077.
  20. Syuan-Rong, H. and Shuo-Jye W. (2011). Bayesian Estimation and Prediction for Weibull Model with Progressive Censoring, J. Stat ComputSimulat, 1-14.
  21. Zellner, A. (1986). Bayesian Estimation and Prediction Using Asymmetric Loss Functions, J. Am Stat Assoc, 81, 446-451.
  22. umass.edu/statdata/statdata/data/pharynx.txt
       

[A. Lavanya and T. Leo Alexander. (2016); ESTIMATION OF PARAMETERS USING LINDLEY’S METHOD. Int. J. of Adv. Res. 4 (Dec). 1767-1780] (ISSN 2320-5407). www.journalijar.com

T. Leo Alexander
Associate Professor

DOI:

Article DOI: 10.21474/IJAR01/2579      
DOI URL: http://dx.doi.org/10.21474/IJAR01/2579

Download Full Paper

Download PDF No. of Downloads: 334 | No. of Views: 738