Improved statistical inference for the two-parameter Birnbaum-Saunders distribution

Computational Statistics and Data Analysis

Volumn 51, Issue 9, 2007, Pages 4656-4681

  Lemonte, Artur J ^a   Cribari Neto, Francisco ^a   Vasconcellos, Klaus L P ^a  

^a FEDERAL UNIVERSITY OF PERNAMBUCO   (Brazil)

Author keywords

Bartlett correction; Bias correction; Birnbaum Saunders distribution; Bootstrap; Interval estimation; Jackknife; Likelihood ratio test; Maximum likelihood estimation

Indexed keywords

DATA REDUCTION; MAXIMUM LIKELIHOOD ESTIMATION; NUMERICAL METHODS; STATISTICAL METHODS;

BARTLETT CORRECTION; BIAS CORRECTION; INTERVAL ESTIMATION; LIKELIHOOD RATIO TESTS; STATISTICAL INFERENCE;

PARAMETER ESTIMATION;

EID: 34147208345     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2006.08.016     Document Type: Article

References (47)

1. Achcar J.A. Inference for the Birnbaum-Saunders fatigue life model using Bayesian methods. Comput. Statist. Data Anal. 15 (1993) 367-380
2. Bartlett M.S. Properties of sufficiency and statistical tests. Proc. Roy. Soc. 160 (1937) 268-282
3. Birnbaum Z.W., and Saunders S.C. A new family of life distributions. J. Appl. Probab. 6 (1969) 319-327
4. Birnbaum Z.W., and Saunders S.C. Estimation for a family of life distributions with applications to fatigue. J. Appl. Prob. 6 (1969) 328-347
5. Buse A. The likelihood ratio, Wald, and Lagrange multiplier tests: an expository note. Amer. Statist. 36 (1982) 153-157
6. Chang D.S., and Tang L.C. Reliability bounds and critical time for the Birnbaum-Saunders distribution. IEEE Trans. Reliability 42 (1993) 464-469
7. Chang D.S., and Tang L.C. Percentile bounds and tolerance limits for the Birnbaum-Saunders distribution. Comm. Statist. Theory Methods 23 (1994) 2853-2863
8. Cohen A.C., Whitten B.J., and Ding Y. Modified moment estimation for the three-parameter Weibull distribution. J. Quality Tech. 16 (1984) 159-167
9. - 1. Biometrika 78 (1991) 573-582
10. Cox D.R., and Snell E. A general definition of residuals. J. Roy. Statist. Soc. B 30 (1968) 248-275
11. Cribari-Neto F., and Cordeiro G.M. On Bartlett and Bartlett-type corrections. Econometric Rev. 15 (1996) 339-367
12. Cribari-Neto F., and Zarkos S.G. Econometric and statistical computing using Ox. Comput. Econom. 21 (2003) 277-295
13. Desmond A.F. Stochastic models of failure in random environments. Canad. J. Statist. 13 (1985) 171-183
14. Desmond A.F. On the relationship between two fatigue-life models. IEEE Trans. Reliability 35 (1986) 167-169
15. Díaz-García J.A., and Leiva-Sánchez V. A new family of life distributions based on the elliptically contoured distributions. J. Statist. Plann. Inference 128 (2005) 445-457
16. DiCiccio T.J., and Tibshirani R. Bootstrap confidence intervals and bootstrap approximations. J. Amer. Statist. Assoc. 82 (1987) 163-170
17. Doornik J.A. Ox: an Object-Oriented Matrix Language. fourth ed (2001), Timberlake Consultants Press, London, Oxford. http://www.doornik.com 〈http://www.doornik.com〉
18. Dupuis D.J., and Mills J.E. Robust estimation of the Birnbaum-Saunders distribution. IEEE Trans. Reliability 47 (1998) 88-95
19. Efron B. Bootstrap methods: another look at the jackknife. Ann. Statist. 7 (1979) 1-26
20. Efron B. Nonparametric standard errors and confidence intervals. Canad. J. Statist. 9 (1981) 139-172
21. Efron, B., 1982. The Jackknife, the Bootstrap and other Resampling Plans. Society for Industrial and Applied Mathematics, Philadelphia.
22. Efron B. Better bootstrap confidence intervals. J. Amer. Statist. Assoc. 82 (1987) 171-200
23. Efron B., and Tibshirani R.J. An Introduction to the Bootstrap (1993), Chapman and Hall, New York
24. Engelhardt M., Bain L.J., and Wright F.T. Inferences on the parameters of the Birnbaum-Saunders fatigue life distribution based on maximum likelihood estimation. Technometrics 23 (1981) 251-256
25. Ferrari S.L.P., and Cribari-Neto F. On the corrections to the Wald test of non-linear restrictions. Econom. Lett. 42 (1993) 321-326
26. Galea M., Leiva-Sánchez V., and Paula G.A. Influence diagnostics in log-Birnbaum-Saunders regression models. J. Appl. Statist. 31 (2004) 1049-1064
27. Hall P. Theoretical comparison of bootstrap confidence intervals. Ann. Statist. 16 (1988) 927-985
28. Jin X., and Kawczak J. Birnbaum-Saunders and lognormal kernel estimators for modelling durations in high frequency financial data. Ann. Econom. Finance 4 (2003) 103-124
29. Johnson, N., Kotz, S., Balakrishnan, N., 1995. Continuous Univariate Distributions. vol. 2, second ed. Wiley, New York.
30. Lawley D. A general method for approximating to the distribution of likelihood ratio criteria. Biometrika 43 (1956) 295-303
31. Lu M., and Chang D.S. Bootstrap prediction intervals for the Birnbaum-Saunders distribution. Microelectron. Reliability 37 (1997) 1213-1216
32. MacKinnon J.G., and Smith J.A.A. Approximate bias correction in econometrics. J. Econometrics 85 (1998) 205-230
33. Mann N.R., Schafer R.E., and Singpurwalla N. Methods for Statistical Analysis of Reliability and Life Data (1974), Wiley, New York
34. McCool, J.I., 1974. Inferential techniques for Weibull populations. Aerospace Research Laboratories Report ARL TR74-0180. Wright-Atterson Air Force Base, Dayton, OH.
35. Mittelhammer R.C., Judge G.G., and Miller D.J. Econometric Foundations (2000), Cambridge University Press, New York
36. Ng H.K.T., Kundu D., and Balakrishnan N. Modified moment estimation for the two-parameter Birnbaum-Saunders distribution. Comput. Statist. Data Anal. 43 (2003) 283-298
37. Owen W.J., and Padgett W.J. Accelerated test models for system strength based on Birnbaum-Saunders distributions. Lifetime Data Anal. 5 (1999) 133-147
38. Owen W.J., and Padgett W.J. A Birnbaum-Saunders accelerated life model. IEEE Trans. Reliability 49 (2000) 224-229
39. Quenouille M. Approximate tests of correlation in time series. J. Roy. Statist. Soc. B 11 (1949) 18-44
40. Rao C.R. Linear Statistical Inference and Its Applications. second ed (1973), Wiley, London
41. Rieck J.R. Parameter estimation for the Birnbaum-Saunders distribution based on symmetrically censored samples. Comm. Statist. Theory Methods 24 (1995) 1721-1736
42. Rieck J.R. A moment-generating function with application to the Birnbaum-Saunders distribution. Comm. Statist. Theory Methods 28 (1999) 2213-2222
43. Rieck J.R., and Nedelman J.R. A log-linear model for the Birnbaum-Saunders distribution. Technometrics 33 (1991) 51-60
44. Saunders S.C. A family of random variables closed under reciprocation. J. Amer. Statist. Assoc. 69 (1974) 533-539
45. Stafford J.E., and Andrews D.F. A symbolic algorithm for studying adjustments to the profile likelihood. Biometrika 80 (1993) 715-730
46. Wang Z., Desmond A.F., and Lu X. Modified censored moment estimation for the two-parameter Birnbaum-Saunders distribution. Comput. Statist. Data Anal. 50 (2006) 1033-1051
47. Wu J., and Wong A.C.M. Improved interval estimation for the two-parameter Birnbaum-Saunders distribution. Comput. Statist. Data Anal. 47 (2004) 809-821