Table of Contents
Journal of Quality and Reliability Engineering
Volume 2013 (2013), Article ID 190437, 13 pages
http://dx.doi.org/10.1155/2013/190437
Research Article

On the Mean Residual Life Function and Stress and Strength Analysis under Different Loss Function for Lindley Distribution

Department of Decision Sciences, Bocconi University, via Roenthen 1, 20136 Milan, Italy

Received 4 November 2012; Accepted 4 February 2013

Academic Editor: Shey-Huei Sheu

Copyright © 2013 Sajid Ali. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. D. V. Lindley, “Fiducial distributions and Bayes' theorem,” Journal of the Royal Statistical Society. Series B, vol. 20, pp. 102–107, 1958. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. M. E. Ghitany, B. Atieh, and S. Nadarajah, “Lindley distribution and its application,” Mathematics and Computers in Simulation, vol. 78, no. 4, pp. 493–506, 2008. View at Publisher · View at Google Scholar · View at Scopus
  3. M. Sankaran, “The discrete Poisson-Lindley distribution,” Biometrics, vol. 26, pp. 145–149, 1970. View at Google Scholar
  4. M. E. Ghitany and D. K. Al-Mutairi, “Estimation methods for the discrete Poisson-Lindley distribution,” Journal of Statistical Computation and Simulation, vol. 79, no. 1, pp. 1–9, 2009. View at Publisher · View at Google Scholar · View at Scopus
  5. M. E. Ghitany, D. K. Al-Mutairi, and S. Nadarajah, “Zero-truncated Poisson-Lindley distribution and its application,” Mathematics and Computers in Simulation, vol. 79, no. 3, pp. 279–287, 2008. View at Publisher · View at Google Scholar · View at Scopus
  6. H. Zamani and N. Ismail, “Negative binomial-Lindley distribution and its application,” Journal of Mathematics and Statistics, vol. 6, no. 1, pp. 4–9, 2010. View at Google Scholar · View at Scopus
  7. M. E. Ghitany, F. Alqallaf, D. K. Al-Mutairi, and H. A. Husain, “A two-parameter weighted Lindley distribution and its applications to survival data,” Mathematics and Computers in Simulation, vol. 81, no. 6, pp. 1190–1201, 2011. View at Publisher · View at Google Scholar · View at Scopus
  8. H. Jeffreys, Theory of Probability, Oxford University Press, 3rd edition, 1964.
  9. A. K. Bansal, Bayesian Parametric Inference, Narosa Publishing House, New Delhi, India, 2007.
  10. M. Wasan, Parametric Estimation, McGraw-Hill, New York, NY, USA, 1970.
  11. K. Kanefuji and K. Iwase, “Estimation for a scale parameter with known coefficient of variation,” Statistical Papers, vol. 39, no. 4, pp. 377–388, 1998. View at Google Scholar · View at Scopus
  12. S. Ali, M. Aslam, and S. M. A. Kazmi, “A study of the effect of the loss function on Bayes Estimate, posterior risk and hazard function for Lindley distribution,” Applied Mathematical Modelling, vol. 37, no. 8, pp. 6078–6078, 2013. View at Publisher · View at Google Scholar
  13. I. Bayramoglu and S. Gurler, “On the mean residual life function of the k-out-of-n system with nonidentical components,” in International Conference on Mathematical and Statistical Modeling in Honor of Enrique Castillo, pp. 28–30, Ciudad Real, Spain, June 2006.
  14. K. K. Govil and K. K. Aggarwal, “Mean residual life function for normal, gamma and lognormal densities,” Reliability Engineering, vol. 5, no. 1, pp. 47–51, 1983. View at Google Scholar · View at Scopus
  15. B. Abdous and A. Berred, “Mean residual life estimation,” Journal of Statistical Planning and Inference, vol. 132, no. 1-2, pp. 3–19, 2005. View at Publisher · View at Google Scholar · View at Scopus
  16. D. V. Lindley, “Approximate Bayesian methods,” Trabajos de Estadistica Y de Investigacion Operativa, vol. 31, no. 1, pp. 223–245, 1980. View at Publisher · View at Google Scholar · View at Scopus
  17. H. A. Howlader and A. M. Hossain, “Bayesian survival estimation of Pareto distribution of the second kind based on failure-censored data,” Computational Statistics and Data Analysis, vol. 38, no. 3, pp. 301–314, 2002. View at Publisher · View at Google Scholar · View at Scopus
  18. R. Singh, S. K. Singh, U. Singh, and G. P. Singh, “Bayes estimator of generalized-exponential parameters under Linex loss function using Lindley's approximation,” Data Science Journal, vol. 7, pp. 65–75, 2008. View at Publisher · View at Google Scholar · View at Scopus
  19. V. Preda, E. Panaitescu, and A. Constantinescu, “Bayes estimators of modified-Weibull distribution parameters using Lindley's approximation,” WSEAS Transactions on Mathematics, vol. 9, no. 7, pp. 539–549, 2010. View at Google Scholar · View at Scopus
  20. M. H. Gail and J. L. Gastwirth, “A scale-free goodness-of-fit test for the exponential distribution based on the Lorenz curve,” Journal of the American Statistical Association, vol. 73, no. 364, pp. 787–793, 1978. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. Z. W. Birnbaum, “On a use of the Mann-Whitney statistic,” in Proceedings of the 3rd Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, pp. 13–17, University of California Press, Berkeley, Calif, USA, 1956. View at MathSciNet
  22. Z. W. Birnbaum and R. C. McCarty, “A distribution-free upper confidence bound for Pr(Y<X), based on independent samples of X and Y,” Annals of Mathematical Statistics, vol. 29, pp. 558–562, 1958. View at Publisher · View at Google Scholar · View at MathSciNet
  23. J. D. Church and B. Harris, “The estimation of reliability from stress strength relationships,” Technometrics, vol. 12, pp. 49–54, 1970. View at Google Scholar
  24. S. Kotz, Y. Lumelskii, and M. Pensky, The Stress-Strength Model and Its Generalizations: Theory and Applications, World Scientific, River Edge, NJ, USA, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  25. D. Kundu and R. D. Gupta, “Estimation of P(Y<X) for Weibull distributions,” IEEE Transactions on Reliability, vol. 55, no. 2, pp. 270–280, 2006. View at Publisher · View at Google Scholar · View at Scopus
  26. D. Kundu and R. D. Gupta, “Estimation of P(Y<X) for generalized exponential distribution,” Metrika, vol. 61, no. 3, pp. 291–308, 2005. View at Publisher · View at Google Scholar · View at Scopus
  27. M. Z. Raqab and D. Kundu, “Comparison of different estimators of P(Y<X) for a scaled Burr type X distribution,” Communications in Statistics: Simulation and Computation, vol. 34, no. 2, pp. 465–483, 2005. View at Publisher · View at Google Scholar · View at Scopus
  28. D. Kundu and M. Z. Raqab, “Estimation of R=P(Y<X) for three-parameter Weibull distribution,” Statistics and Probability Letters, vol. 79, no. 17, pp. 1839–1846, 2009. View at Publisher · View at Google Scholar · View at Scopus
  29. K. Krishnamoorthy, S. Mukherjee, and H. Guo, “Inference on reliability in two-parameter exponential stress-strength model,” Metrika, vol. 65, no. 3, pp. 261–273, 2007. View at Publisher · View at Google Scholar · View at Scopus
  30. S. Eryilmaz, “On system reliability in stress-strength setup,” Statistics and Probability Letters, vol. 80, no. 9-10, pp. 834–839, 2010. View at Publisher · View at Google Scholar · View at Scopus
  31. D. K. Al-Mutairi, M. E. Ghitany, and D. Kundu, “Inferences on stress-strength reliability from Lindley distribution,” to appear in Communications in Statistics—Theory and Methods, available from http://home.iitk.ac.in/~kundu/lindley-ss.pdf.