On Bayesian Analysis of Failure Rate under Topp Leone Distribution using Complete and Censored Samples
The article is concerned with analysis of failure rate (shape parameter) under the Topp Leone distribution using a Bayesian framework. Different loss functions and a couple of noninformative priors have been assumed for posterior estimation. The posterior predictive distributions have also been derived. A simulation study has been carried to compare the performance of different estimators. A real life example has been used to illustrate the applicability of the results obtained. The findings of the study suggest that the precautionary loss function based on Jeffreys prior and singly type II censored samples can effectively be employed to
obtain the Bayes estimate of the failure rate under Topp Leone distribution.
<p>[1] C. W. Topp, and F. C. Leone, “A family of J-shaped frequency
functions,” Journal of the American Statistical Association, vol. 50,
pp.209–219, 1955.
[2] S. Nadarajah, and S. Kotz, “Moments of some J-shaped distribution,”
Journal of Applied Statistics, vol. 30, pp. 311–317, 2003.
[3] D. Vicari, J. R. V. Dorp, and S. Kotz, “Two-sided generalized Topp and
Leone (TS-GTL) distributions,” Journal of Applied Statistics, vol. 35,
no. 10, pp. 1115–1129, 2008.
[4] Gen, and Ali, “Moments of order statistics of Topp-Leone distribution,”
Statistical Papers, vol. 53, no. 1, pp. 117–121, 2012.
[5] P. S. Laplace, Theorie Analytique Des Probabilities. Veuve Courcier
Paris, 1812.
[6] H. Jeffreys, Theory of Probability. 3rd edn: Oxford University Press,
1961, pp. 432.
[7] J. W. Wu, and S. H. Lin, “Interval estimation of the Weibull distribution
under the failure-censored sampling plan,” Information and Management
Sciences, vol. 12, no. 2, pp. 39–50, 2001.
[8] A. J. Fermindez, J. I. Bravo, and F. D. Fuentes, “Computing maximum
likelihood estimates from Type II doubly censored exponential data,”
Statistical Methods & Applications, vol. 11, pp. 187–200, 2002.
[9] M. Z. Raqab, and M. T. Madi, “Bayesian prediction of the total time on
test using doubly censored Rayleigh data,” J. Statist. Comput. Simul.,
vol. 72, no. 10, pp. 781–789, 2002.
[10] A. Fauzy, “Interval estimation for parameters of exponential distribution
under doubly type II censoring,” Journal of Applies Mathematics, vol.
10, pp. 71–79, 2004.
[11] M. Saleem, and M. Aslam, “On Bayesian analysis of the Rayleigh
survival time assuming the random censored time,” Pakistan Journal of
Statistics, vol. 25, no. 2, pp. 71–82, 2009.
[12] A. Asgharzadeh, and R. Valiollahi, “Estimation based on progressively
censored data from the Burr model,” International Mathematical Forum,
vol. 3, pp. 2113–2121, 2008.
[13] A. S. Akhter, and A. S. Hirai, “Estimation of the scale parameter from
the Rayleigh distribution from type II singly and doubly censored data,”
Pak.j.stat.opr.res., vol. 5, no. 1, pp. 31–45, 2009.
[14] M. Yarmohammadi, and H. Pazira, “Classical and Bayesian estimations
on the generalized exponential distribution using censored data,” Int. J.
of Math. Analysis, vol. 4, pp. 1417–1431, 2010.
[15] E. J. AL-Hussaini, and M. Hussein, “Estimation using censored data
from exponentiated Burr type XII population,” American Open Journal
of Statistics, vol.1, pp. 33–45, 2011.
[16] N. Feroze, and M. Aslam, “Bayesian analysis of Gumbel type ii
distribution under doubly censored samples using different loss
functions,” Caspian Journal of Applied Sciences Research, vol. 1, no.
10, pp. 1–10, 2012.
[17] N. Feroze, and M. Aslam, “Bayesian analysis of Burr type x distribution
under complete and censored samples,” International Journal of Pure
and Applied Sciences and Technology, vol. 11, no. 2, pp. 16–28, 2012.
[18] N. Feroze, and M. Aslam, “On Bayesian analysis of Burr type vii
distribution under different censoring schemes,” International Journal of
Quality, Statistics, and Reliability, vol. 3, pp. 1–5, 2012.
[19] E. L. Butler, “Estimating the survival distribution of aluminum
processing pots,” Carnegie Mellon University Research Showcase,
2011.</p>
<p>[1] C. W. Topp, and F. C. Leone, “A family of J-shaped frequency
functions,” Journal of the American Statistical Association, vol. 50,
pp.209–219, 1955.
[2] S. Nadarajah, and S. Kotz, “Moments of some J-shaped distribution,”
Journal of Applied Statistics, vol. 30, pp. 311–317, 2003.
[3] D. Vicari, J. R. V. Dorp, and S. Kotz, “Two-sided generalized Topp and
Leone (TS-GTL) distributions,” Journal of Applied Statistics, vol. 35,
no. 10, pp. 1115–1129, 2008.
[4] Gen, and Ali, “Moments of order statistics of Topp-Leone distribution,”
Statistical Papers, vol. 53, no. 1, pp. 117–121, 2012.
[5] P. S. Laplace, Theorie Analytique Des Probabilities. Veuve Courcier
Paris, 1812.
[6] H. Jeffreys, Theory of Probability. 3rd edn: Oxford University Press,
1961, pp. 432.
[7] J. W. Wu, and S. H. Lin, “Interval estimation of the Weibull distribution
under the failure-censored sampling plan,” Information and Management
Sciences, vol. 12, no. 2, pp. 39–50, 2001.
[8] A. J. Fermindez, J. I. Bravo, and F. D. Fuentes, “Computing maximum
likelihood estimates from Type II doubly censored exponential data,”
Statistical Methods & Applications, vol. 11, pp. 187–200, 2002.
[9] M. Z. Raqab, and M. T. Madi, “Bayesian prediction of the total time on
test using doubly censored Rayleigh data,” J. Statist. Comput. Simul.,
vol. 72, no. 10, pp. 781–789, 2002.
[10] A. Fauzy, “Interval estimation for parameters of exponential distribution
under doubly type II censoring,” Journal of Applies Mathematics, vol.
10, pp. 71–79, 2004.
[11] M. Saleem, and M. Aslam, “On Bayesian analysis of the Rayleigh
survival time assuming the random censored time,” Pakistan Journal of
Statistics, vol. 25, no. 2, pp. 71–82, 2009.
[12] A. Asgharzadeh, and R. Valiollahi, “Estimation based on progressively
censored data from the Burr model,” International Mathematical Forum,
vol. 3, pp. 2113–2121, 2008.
[13] A. S. Akhter, and A. S. Hirai, “Estimation of the scale parameter from
the Rayleigh distribution from type II singly and doubly censored data,”
Pak.j.stat.opr.res., vol. 5, no. 1, pp. 31–45, 2009.
[14] M. Yarmohammadi, and H. Pazira, “Classical and Bayesian estimations
on the generalized exponential distribution using censored data,” Int. J.
of Math. Analysis, vol. 4, pp. 1417–1431, 2010.
[15] E. J. AL-Hussaini, and M. Hussein, “Estimation using censored data
from exponentiated Burr type XII population,” American Open Journal
of Statistics, vol.1, pp. 33–45, 2011.
[16] N. Feroze, and M. Aslam, “Bayesian analysis of Gumbel type ii
distribution under doubly censored samples using different loss
functions,” Caspian Journal of Applied Sciences Research, vol. 1, no.
10, pp. 1–10, 2012.
[17] N. Feroze, and M. Aslam, “Bayesian analysis of Burr type x distribution
under complete and censored samples,” International Journal of Pure
and Applied Sciences and Technology, vol. 11, no. 2, pp. 16–28, 2012.
[18] N. Feroze, and M. Aslam, “On Bayesian analysis of Burr type vii
distribution under different censoring schemes,” International Journal of
Quality, Statistics, and Reliability, vol. 3, pp. 1–5, 2012.
[19] E. L. Butler, “Estimating the survival distribution of aluminum
processing pots,” Carnegie Mellon University Research Showcase,
2011.</p>
@article{"International Journal of Engineering, Mathematical and Physical Sciences:65129", author = "N. Feroze and M. Aslam", title = "On Bayesian Analysis of Failure Rate under Topp Leone Distribution using Complete and Censored Samples", abstract = "The article is concerned with analysis of failure rate (shape parameter) under the Topp Leone distribution using a Bayesian framework. Different loss functions and a couple of noninformative priors have been assumed for posterior estimation. The posterior predictive distributions have also been derived. A simulation study has been carried to compare the performance of different estimators. A real life example has been used to illustrate the applicability of the results obtained. The findings of the study suggest that the precautionary loss function based on Jeffreys prior and singly type II censored samples can effectively be employed to
obtain the Bayes estimate of the failure rate under Topp Leone distribution.
", keywords = "loss functions, type II censoring, posterior
distribution, Bayes estimators.", volume = "7", number = "3", pages = "402-7", }
