JOURNAL BROWSE
Search
Advanced SearchSearch Tips
Noninformative Priors for the Stress-Strength Reliability in the Generalized Exponential Distributions
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
Noninformative Priors for the Stress-Strength Reliability in the Generalized Exponential Distributions
Kang, Sang-Gil; Kim, Dal-Ho; Lee, Woo-Dong;
  PDF(new window)
 Abstract
This paper develops the noninformative priors for the stress-strength reliability from one parameter generalized exponential distributions. When this reliability is a parameter of interest, we develop the first, second order matching priors, reference priors in its order of importance in parameters and Jeffreys` prior. We reveal that these probability matching priors are not the alternative coverage probability matching prior or a highest posterior density matching prior, a cumulative distribution function matching prior. In addition, we reveal that the one-at-a-time reference prior and Jeffreys` prior are actually a second order matching prior. We show that the proposed reference prior matches the target coverage probabilities in a frequentist sense through a simulation study and a provided example.
 Keywords
Generalized exponential model;matching prior;reference prior;stress-strength reliability;
 Language
English
 Cited by
 References
1.
Baklizi, A. (2008). Likelihood and Bayesian estimation of Pr(X < Y) using lower record values from the generalized exponential distribution, Computational Statistics and Data Analysis, 52, 3468-3473. crossref(new window)

2.
Berger, J. O. and Bernardo, J. M. (1989). Estimating a product of means: Bayesian Analysis with Reference Priors, Journal of the American Statistical Association, 84, 200-207. crossref(new window)

3.
Berger, J. O. and Bernardo, J. M. (1992). On the development of reference priors (with discussion), Bayesian Statistics IV, J. M. Bernardo, et al., Oxford University Press, Oxford, 35-60.

4.
Bernardo, J. M. (1979). Reference posterior distributions for Bayesian inference (with discussion), Journal of Royal Statistical Society, Series B, 41, 113-147.

5.
Cox, D. R. and Reid, N. (1987). Orthogonal parameters and approximate conditional inference (with discussion), Journal of Royal Statistical Society, Series B, 49, 1-39.

6.
Datta, G. S. and Ghosh, J. K. (1995a). On priors providing frequentist validity for Bayesian inference, Biometrika, 82, 37-45. crossref(new window)

7.
Datta, G. S. and Ghosh, M. (1995b). Some remarks on noninformative priors, Journal of the American Statistical Association, 90, 1357-1363. crossref(new window)

8.
Datta, G. S. and Ghosh, M. (1996). On the invariance of noninformative priors, The Annals of Statistics, 24, 141-159. crossref(new window)

9.
Datta, G. S., Ghosh, M. and Mukerjee, R. (2000). Some new results on probability matching priors, Calcutta Statistical Association Bulletin, 50, 179-192.

10.
DiCiccio, T. J. and Stern, S. E. (1994). Frequentist and Bayesian bartlett correction of test statistics based on adjusted profile likelihood, Journal of Royal Statistical Society, Series B, 56, 397-408.

11.
Ghosh, J. K. and Mukerjee, R. (1992). Noninformative priors (with discussion), Bayesian Statistics IV, J.M. Bernardo, et. al., Oxford University Press, Oxford, 195-210.

12.
Ghosh, J. K. and Mukerjee, R. (1995). Frequentist validity of highest posterior density regions in the presence of nuisance parameters, Statistics & Decisions, 13, 131-139.

13.
Gupta, R. and Kundu, D. (1999). Generalized exponential distributions, Australian and New Zealand Journal of Statistics, 41, 173-188. crossref(new window)

14.
Gupta, R. and Kundu, D. (2001). Generalized exponential distribution, an alternative to gamma and Weibull distribution, Biometrical Journal, 43, 117-130. crossref(new window)

15.
Kang, S. G., Kim, D. H. and Lee,W. D. (2011). Noninformative priors for stress-strength reliability in the Pareto distributions, Journal of the Korean Data & Information Science Society, 22, 115-123.

16.
Kim, D. H., Kang, S. G. and Lee,W. D. (2009). Noninformative priors for Pareto distribution, Journal of the Korean Data & Information Science Society, 20, 1213-1223.

17.
Kundu, D. and Gupta, R. (2005). Estimation of P[Y < X] for generalized exponential distribution, Metrika, 61, 291-308. crossref(new window)

18.
Kundu, D. and Gupta, R. (2007). Generalized exponential distribution: Existing results and some recent developments, Journal of Statistical Planning and Inference, 136, 3130-3144.

19.
Mukerjee, R. and Dey, D. K. (1993). Frequentist validity of posterior quantiles in the presence of a nuisance parameter: Higher order asymptotics, Biometrika, 80, 499-505. crossref(new window)

20.
Mukerjee, R. and Ghosh, M. (1997). Second order probability matching priors, Biometrika, 84, 970-975. crossref(new window)

21.
Mukerjee, R. and Ghosh, M. (1997). Second order probability matching priors, Biometrika, 84, 970-975. crossref(new window)

22.
Raqab, M. Z. and Madi, M. T. (2005). Bayesian inference for the generalized exponential distribution, Journal of Statistical Computation and Simulation, 75, 841-852. crossref(new window)

23.
Stein, C. (1985). On the coverage probability of confidence sets based on a prior distribution, Sequential Methods in Statistics, Banach Center Publications, 16, 485-514.

24.
Tibshirani, R. (1989). Noninformative priors for one parameter of many, Biometrika, 76, 604-608. crossref(new window)

25.
Welch, B. L. and Peers, H. W. (1963). On formulae for confidence points based on integrals of weighted likelihood, Journal of Royal Statistical Society, Series B, 25, 318-329.

26.
Wong, A. C. M. and Wu, Y. Y. (2009). A note on interval estimation P(X < Y) using lower record data from the generalized exponential distribution, Computational Statistics and Data Analysis, 53, 3650-3658. crossref(new window)