×
Achcar, Jorge A.; Coelho-Barros, Emílio A.; Cordeiro, Gauss M.

Beta generalized distributions and related exponentiated models: a Bayesian approach. (English) Zbl 1319.62027

Braz. J. Probab. Stat. 27, No. 1, 1-19 (2013).
Summary: We introduce a Bayesian analysis for beta generalized distributions and related exponentiated models. We review the exponentiated exponential, exponentiated Weibull and beta generalized exponential distributions. These distributions have been proposed as alternative extensions of the gamma and Weibull distributions in the analysis of lifetime data. Some posterior summaries of interest are obtained using Monte Carlo Markov chain (MCMC) methods. An application to a real data set is given to illustrate the potentiality of the Bayesian analysis.

Cited in 3 Documents

MSC:

62E15 Exact distribution theory in statistics
62F15 Bayesian inference
62N05 Reliability and life testing

Keywords:

beta generalized exponential distribution; exponentiated exponential distribution; exponentiated Weibull distribution; information matrix; maximum likelihood estimation

Software:

BUGS
PDF BibTeX XML Cite
\textit{J. A. Achcar} et al., Braz. J. Probab. Stat. 27, No. 1, 1--19 (2013; Zbl 1319.62027)
Full Text: DOI Euclid
  • logo of hbz
  • logo of WorldCat

References:

[1] Akaike, H. (1973). Information Theory and an Extension of the Maximum Likelihood Principle : Proceedings of the 2nd International Symposium on Information Theory (N. Petrov and F. Caski, eds.). Budapest: Adadémiai Kiadó. · Zbl 0283.62006
[2] Akaike, H. (1974). A new look at statistical model identification. IEEE Transactions Automatic Control 19 , 716-722. · Zbl 0314.62039
[3] Barreto-Souza, W., Santos, A. and Cordeiro, G. M. (2010). The beta generalized exponential distribution. Journal of Statistical Computation and Simulation 80 , 159-172. · Zbl 1184.62012
[4] Berg, A., Meyer, R. and Yu, J. (2004). Deviance information criterion for comparing stochastic volatility models. Journal of Business & Economic Statistics 22 , 107-120.
[5] Box, G. E. and Tiao, G. C. (1973). Bayesian Inference in Statistical Analysis . New York: Addison-Wesley. · Zbl 0271.62044
[6] Brooks, S. P. (2002). Discussion on the paper by Spiegelhalter, Best, Carlin and Van de Linde (2002). Journal of the Royal Statistical Society, Ser. B 64 , 616-618.
[7] Celeux, G., Forbes, F., Robert, C. P. and Titterington, D. M. (2005). Deviance information criteria for missing data models. Bayesian Analysis 1 , 651-674. · Zbl 1331.62329
[8] Cordeiro, G. M., Simas, A. B. and Stosic, B. (2011). Closed form expressions for moments of the beta Weibull distribution. Anais da Academia Brasileira de Ciências 83 , 357-373. · Zbl 1221.62026
[9] Eugene, N., Lee, C. and Famoye, F. (2002). Beta-normal distribution and its applications. Communication in Statistics-Theory and Methods 31 , 497-512. · Zbl 1009.62516
[10] Gelfand, A. E., Dey, D. K. and Chang, H. (1992). Model determination using predictive distributions with implementation via sampling-based methods. In Bayesian Statistics 147-167. New York: Oxford Univ. Press.
[11] Gelfand, A. E. and Smith, A. F. M. (1990). Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association 85 , 398-409. · Zbl 0702.62020
[12] Gupta, R. C., Gupta, P. L. and Gupta, R. D. (1998). Modeling failure time data by Lehman alternatives. Communication in Statistics-Theory and Methods 27 , 887-904. · Zbl 0900.62534
[13] Gupta, R. D. and Kundu, D. (2001). Exponentiated exponential family: An alternative to gamma and Weibull distributions. Biometrical Journal 43 , 117-130. · Zbl 0997.62076
[14] Gupta, R. D. and Kundu, D. (1999). Generalized exponential distributions. Australian & New Zealand Journal of Statistics 41 , 173-188. · Zbl 1007.62503
[15] Gupta, R. D. and Kundu, D. (2001). Exponentiated exponential family: An alternative to gamma and Weibull distributions. Biometrical Journal 43 , 117-130. · Zbl 0997.62076
[16] Gupta, A. K. and Nadarajah, S. (2004). On the moments of the beta normal distribution. Communication in Statistics-Theory and Methods 33 , 1-13. · Zbl 1210.60018
[17] Jones, M. C. (2004). Families of distributions arising from distributions of order statistics. Test 13 , 1-43. · Zbl 1110.62012
[18] Kundu, D. and Gupta, R. D. (2007). A convenient way of generating gamma random variables using generalized exponential distribution. Computational Statistics & Data Analysis 51 , 2796-2802. · Zbl 1161.65306
[19] Kundu, D. and Gupta, R. D. (2008). Generalized exponential distribution: Bayesian estimations. Computational Statistics & Data Analysis 52 , 1873-1883. · Zbl 1452.62182
[20] Lawless, J. F. (1982). Statistical Models and Methods for Lifetime Data . New York: Wiley. · Zbl 0541.62081
[21] Lieblein, J. and Zelen, M. (1956). Statistical investigation of the fatigue life of deep groove ball bearings. Journal of Research of the National Bureau Standards 57 , 273-316.
[22] Mudholkar, G. S. and Hutson, A. D. (1996). The exponentiated Weibull family: Some properties and a flood data application. Communication in Statistics-Theory and Methods 25 , 3059-3083. · Zbl 0887.62019
[23] Mudholkar, G. S. and Srivastava, D. K. (1993). Exponentiated Weibull family for analysing bathtub failure data. IEEE Transactions on Reliability 42 , 299-302. · Zbl 0800.62609
[24] Mudholkar, G. S., Srivastava, D. K. and Freimer, M. (1995). The exponentiated Weibull family. Technometrics 37 , 436-445. · Zbl 0900.62531
[25] Nadarajah, S. and Kotz, S. (2004). The beta Gumbel distribution. Mathematical Problems in Engineering 10 , 323-332. · Zbl 1068.62012
[26] Nadarajah, S. and Kotz, S. (2005). The beta exponential distribution. Reliability Engineering and System Safety 91 , 689-697. · Zbl 1079.33011
[27] Nadarajah, S. and Kotz, S. (2006). The exponentiated type distributions. Acta Applicandae Mathematicae 92 , 97-111. · Zbl 1128.62015
[28] Nassar, M. M. and Eissa, F. H. (2003). On the exponentiated Weibull distribution. Communication in Statistics-Theory and Methods 32 , 1317-1336. · Zbl 1140.62308
[29] Raqab, M. Z. (2002). Inferences for generalized exponential distribution based on record statistics. Journal of Statistical Planning and Inference 104 , 339-350. · Zbl 0992.62013
[30] Raqab, M. Z. and Ahsanullah, M. (2001). Estimation of the location and scale parameters of generalized exponential distribution based on order statistics. Journal of Statistical Computation and Simulation 69 , 109-124. · Zbl 1151.62309
[31] Rue, H., Martino, S. and Chopin, N. (2009). Approximete Bayesian inference for latent Gaussian models using integrated nested Laplace approximations (with discussion). Journal of the Royal Statistical Society, Ser. B 71 , 319-392. · Zbl 1248.62156
[32] Smith, A. F. M. and Roberts, G. O. (1993). Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods. Journal of the Royal Statistical Society, Ser. B 55 , 3-23. · Zbl 0779.62030
[33] Spiegelhalter, D. J., Best, N. G. and Vander Linde, A. (2000). A Bayesian measure of model complexity and fit (with discussion). Journal of the Royal Statistical Society, Ser. B 64 , 583-639. · Zbl 1067.62010
[34] Spiegelhalter, D. J., Thomas, A., Best, N. G. and Gilks, W. R. (1995). BUGS: Bayesian Inference Using Gibbs Sampling, Version 0.50 . Cambridge: MRC Biostatistics Unit.
[35] Surles, J. G. and Padgett, W. J. (2001). Inference for reliability and stress-strength for a scaled Burr type X distribution. Lifetime Data Analysis 7 , 187-200. · Zbl 0984.62082
[36] Zheng, G. (2002). Fisher information matrix in type-II censored data from exponentiated exponential family. Biometrical Journal 44 , 353-357. · Zbl 04572175
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.