On Birnbaum-Saunders inference

Computational Statistics and Data Analysis

Volumn 52, Issue 11, 2008, Pages 4939-4950

  Cysneiros, Audrey H M A ^a   Cribari Neto, Francisco ^a   Araújo Jr , Carlos A G ^a  

^a DEPARTAMENTO DE QUÍMICA FUNDAMENTAL   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

FUNCTION EVALUATION; MAXIMUM LIKELIHOOD; OPTIMIZATION; PARAMETER ESTIMATION;

LIKELIHOOD FUNCTION; SHAPE PARAMETER;

FATIGUE OF MATERIALS;

EID: 45049087476     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2008.04.003     Document Type: Article

References (31)

1. Barndorff-Nielsen O.E. On a formula for the distribution of the maximum likelihood estimator. Biometrika 70 (1983) 343-365
2. Barndorff-Nielsen O.E. Adjusted versions of profile likelihood and directed likelihood, and extended likelihood. Journal of the Royal Statistical Society B 56 (1994) 125-140
3. Bhattacharyya G.K., and Fries A. Fatigue failure models - Birnbaum-Saunders vs. inverse Gaussian. IEEE Transactions on Reliability 31 (1982) 439-440
4. Birnbaum Z.W., and Saunders S.C. A new family of life distribution. Journal of Applied Probability 6 (1969) 319-327
5. Birnbaum Z.W., and Saunders S.C. Estimation for a family of life distributions with applications to fatigue. Journal of Applied Probability 6 (1969) 328-347
6. Cohen A.C., Whitten B.J., and Ding Y. Modified moment estimation for the three-parameter Weibull distribution. Journal of Quality Technology 16 (1984) 159-167
7. Cox D.R., and Reid N. Parameter orthogonality and approximate conditional inference. Journal of the Royal Statistical Society B 49 (1987) 1-39
8. Cox D.R., and Reid N. A note on the difference between profile and modified profile likelihood. Biometrika 79 (1992) 408-411
9. Cribari-Neto F., and Cordeiro G.M. On Bartlett and Bartlett-type corrections. Econometric Reviews 15 (1996) 339-367
10. Desmond A.F. Stochastic models of failure in random environments. Canadian Journal of Statistics 13 (1985) 171-183
11. Desmond A.F. On the relationship between two fatigue-life models. IEEE Transactions on Reliability 35 (1986) 167-169
12. Doornik J.A. An Object-oriented Matrix Programming Language-Ox4 (2006), Timberlake Consultants, London. http://www.doornik.com
13. 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
14. Fletcher H. A verification of the theory of Brownian movements and a direct determination of the value of NE for gaseous ionization. The Physical Review 33 (1911) 81-110
15. From S.G., and Li L. Estimation of the parameters of the Birnbaum-Saunders distribution. Communications in Statistics-Theory and Methods 35 (2006) 2157-2169
16. Freudenthal, A.M., Shinozuka, M., 1961. Structural safety under conditions of ultimate load failure and fatigue. Technical report WADD-TR-61-77. Wight Air Development Division
17. Konstantinowsky D. Elektrische Ladungen und Brown'sche Bewegung sehr kleiner Metallteilchen in Gasen. Sitzungsberitchte der Kaiserlichen Akademie der Wissenschaften 123 (1914) 1697-1752
18. Kundu D., Kannan N., and Balakishnan N. On the hazard function of Birnbaum-Saunders distribution and associated inference. Computational Statistics and Data Analysis 52 (2008) 2692-2702
19. Lemonte A.J., Cribari-Neto F., and Vasconcellos K.L.P. Improved statistical inference for the two-parameter Birnbaum-Saunders distribution. Computational Statistics and Data Analysis 51 (2007) 4656-4681
20. Marshall A.W., and Olkin I. Life Distributions: Structure of Nonparametric, Semiparametric and Parametric Families (2007), Springer, New York
21. McCool, J.I., 1974. Inferential techniques for Weibull populations. Aerospace Research Laboratories Report. ARL TR74-0180. Wright-Patterson Air Force Base, Dayton, OH
22. McCullagh P., and Tibishirani R. A simple method for the adjustment of profile likelihood. Journal of the Royal Statistical Society B 52 (1990) 325-344
23. Ng H.K.T., Kundu D., and Balakrishnan N. Modified moment estimation for the two-parameter Birnbaum-Saunders distribution. Computational Statistics and Data Analysis 43 (2003) 283-298
24. Nocedal J., and Wright S.J. Numerical Optimization (1999), Springer, New York
25. Pace L., and Salvan A. Principles of Statistical Inference from a Neo-Fisherian Perspective (1997), World Scientific, Singapore
26. Saunders S.C. A family of random variables closed under reciprocation. Journal of the American Statistical Association 69 (1974) 533-539
27. Schrödinger E. Zür Theorie der Fall-und Steigversuche an Teilchenn mit Brownscher Bewegung. Physikalische Zeitschrift 16 (1915) 289-295
28. Severini T.A. An approximation to the modified profile likelihood function. Biometrika 85 (1998) 403-411
29. Severini T.A. An empirical adjustment to the likelihood ratio statistic. Biometrika 86 (1999) 235-247
30. Severini T.A. Likelihood Methods in Statistics (2000), Oxford University Press, Oxford
31. Stern S.E. A second-order adjustment to the profile likelihood in the case of a multidimensional parameter of interest. Journal of the Royal Statistical Society B 59 (1997) 653-665