The beta generalized gamma distribution

Statistics

Volumn 47, Issue 4, 2013, Pages 888-900

  Cordeiro, Gauss M ^a   Castellares, Fredy ^b   Montenegro, Lourdes C ^b   de Castro, Mário ^c  

^a FEDERAL UNIVERSITY OF PERNAMBUCO   (Brazil)

^b FEDERAL UNIVERSITY OF MINAS GERAIS   (Brazil)

^c UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

beta generalized distribution; expected information matrix; generalized gamma distribution; mean deviation; moment

Indexed keywords

EID: 84884480787     PISSN: 02331888     EISSN: 10294910     Source Type: Journal    
DOI: 10.1080/02331888.2012.658397     Document Type: Article

References (34)

1. Stacy, E. W. 1962. A generalization of the gamma distribution. Ann. Math. Statist, 33: 1187 - 1192. (doi:10.1214/aoms/1177704481)
2. Stacy, E. W. and Mihram, G. A. 1965. Parameter estimation for a generalized gamma distribution. Technometrics, 7: 349 - 358. (doi:10.1080/00401706.1965.10490268)
3. Harter, H. L. 1967. Maximum-likelihood estimation of the parameters of a four-parameter generalized gamma population from complete and censored samples. Technometrics, 9: 159 - 165. (doi:10.1080/00401706.1967.10490449)
4. Hager, H. W. and Bain, L. J. 1970. Inferential procedures for the generalized gamma distribution. J. Amer. Statist. Assoc, 65: 1601 - 1609. (doi:10.1080/01621459.1970.10481190)
5. Prentice, R. L. 1974. A log gamma model and its maximum likelihood estimation. Biometrika, 61: 539 - 544. (doi:10.1093/biomet/61.3.539)
6. Lawless, J. F. 1980. Inference in the generalized gamma and log gamma distributions. Technometrics, 22: 409 - 419. (doi:10.1080/00401706.1980.10486173)
7. DiCiccio, T. J. 1987. Approximate inference for the generalized gamma distribution. Technometrics, 29: 33 - 40. (doi:10.1080/00401706.1987.10488181)
8. Huang, P.-H. and Hwang, T.-Y. 2006. On new moment estimation of parameters of the generalized gamma distribution using it's characterization. Taiwanese J. Math, 10: 1083 - 1093.
9. Cox, C., Chu, H., Schneider, M. F. and Muñoz, A. 2007. Parametric survival analysis and taxonomy of hazard functions for the generalized gamma distribution. Stat. Med, 26: 4352 - 4374. (doi:10.1002/sim.2836)
10. Almpanidis, G. and Kotropoulos, C. 2008. Phonemic segmentation using the generalised Gamma distribution and small sample Bayesian information criterion. Speech Commun, 50: 38 - 55. (doi:10.1016/j.specom.2007.06.005)
11. Nadarajah, S. 2008. On the use of the generalised gamma distribution. Int. J. Electron, 95: 1029 - 1032. (doi:10.1080/00207210802354981)
12. Gomes, O., Combes, C. and Dussauchoy, A. 2008. Parameter estimation of the generalized gamma distribution. Math. Comput. Simul, 79: 955 - 963. (doi:10.1016/j.matcom.2008.02.006)
13. Tadikamalla, P. R. 1979. Random sampling from the generalized gamma distribution. Computing, 23: 199 - 203. (doi:10.1007/BF02252098)
14. Eugene, N., Lee, C. and Famoye, F. 2002. Beta-normal distribution and its applications. Comm. Statist. Theory Methods, 31: 497 - 512. (doi:10.1081/STA-120003130)
15. Mudholkar, G. S., Srivastava, D. K. and Freimer, M. 1995. The exponentiated Weibull family - A reanalysis of the bus- motor-failure data. Technometrics, 37: 436 - 445. (doi:10.1080/00401706.1995.10484376)
16. Gupta, R. D. and Kundu, D. 2001. Exponentiated exponential family: An alternative to gamma and Weibull distributions. Biom. J, 43: 117 - 130. (doi:10.1002/1521-4036(200102)43:1<117::AID-BIMJ117>3.0.CO;2-R)
17. Nadarajah, S. and Kotz, S. 2004. The beta Gumbel distribution. Math. Probl. Eng, 10: 323 - 332. (doi:10.1155/S1024123X04403068)
18. Nadarajah, S. and Gupta, A. K. 2004. The beta Fréchet distribution. Far East J. Theor. Stat, 14: 15 - 24.
19. Nadarajah, S. and Kotz, S. 2006. The beta exponential distribution. Reliab. Eng. Syst. Saf, 91: 689 - 697. (doi:10.1016/j.ress.2005.05.008)
20. Pescim, R. R., Demétrio, C. G.B., Cordeiro, G. M., Ortega, E. M.M. and Urbano, M. R. 2010. The beta generalized half-normal distribution. Comput. Statist. Data Anal, 54: 945 - 957. (doi:10.1016/j.csda.2009.10.007)
21. Cooray, K. and Ananda, M. M.A. 2008. A generalization of the half-normal distribution with applications to lifetime data. Comm. Statist. Theory Methods, 37: 1323 - 1337. (doi:10.1080/03610920701826088)
22. Paranaíba, P. F., Ortega, E. M.M., Cordeiro, G. M. and Pescim, R. R. 2011. The beta Burr XII distribution with application to lifetime data. Comput. Statist. Data Anal, 55: 1118 - 1136. (doi:10.1016/j.csda.2010.09.009)
23. Zografos, K. and Balakrishnan, N. 2009. On the families of beta-and generalized gamma-generated distribution and associated inference. Stat. Methodol, 6: 344 - 362. (doi:10.1016/j.stamet.2008.12.003)
24. Lee, C., Famoye, F. and Olumolade, O. 2007. Beta-Weibull distribution: Some properties and applications to censored data. J. Mod. Appl. Stat. Methods, 6: 173 - 186.
25. Kong, L., Lee, C. and Sepanski, J. H. 2007. On the properties of beta-gamma distribution. J. Mod. Appl. Stat. Methods, 6: 187 - 211.
26. Cordeiro, G. M. and Nadarajah, S. 2009. " General results for beta Weibull distribution ". Manuscript in preparation
27. R Development Core Team. 2011. " R: A Language and Environment for Statistical Computing ". Vienna, Austria: R Foundation for Statistical Computing.
28. Smith, R. L. and Naylor, J. C. 1987. A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distribution. Appl. Stat, 36: 323 - 332.
29. Dunn, P. K. and Smyth, G. K. 1996. Randomized quantile residuals. J. Comput. Graph. Statist, 5: 236 - 244.
30. Barreto-Souza, W., Santos, A. and Cordeiro, G. M. 2010. The beta generalized exponential distribution. J. Stat. Comput. Simul, 80: 159 - 172. (doi:10.1080/00949650802552402)
31. Mudholkar, G. S. and Hutson, A. D. 1996. The exponentiated Weibull family: Some properties and a flood data application. Comm. Statist. Theory Methods, 25: 3059 - 3083. (doi:10.1080/03610929608831886)
32. Nassar, M. M. and Eissa, F. H. 2003. On the exponentiated Weibull distribution. Comm. Statist. Theory Methods, 32: 1317 - 1336. (doi:10.1081/STA-120021561)
33. Choudhury, A. 2005. A simple derivation of moments of the exponentiated Weibull distribution. Metrika, 62: 17 - 22. (doi:10.1007/s001840400351)
34. Nadarajah, S. and Gupta, A. K. 2005. On the moments of the exponentiated Weibull distribution. Comm. Statist. Theory Methods, 34: 253 - 256.