A new fatigue life model based on the family of skew-elliptical distributions

Communications in Statistics - Theory and Methods

Volumn 35, Issue 2, 2006, Pages 229-244

  Vilca Labra, Filidor ^a   Leiva Sánchez, Víctor ^b  

^a UNIVERSITY OF CAMPINAS   (Brazil)

^b UNIVERSIDAD DE VALPARAÍSO   (Chile)

Author keywords

Birnbaum Saunders distribution; Kurtosis; Life distributions; Material fatigue; Moments; Reliability analysis; Skew elliptical distributions; Skewness

Indexed keywords

PROBABILITY DENSITY FUNCTION; RELIABILITY; STRUCTURAL ANALYSIS;

BIRNBAUM-SAUNDERS DISTRIBUTION; LIFE DISTRIBUTIONS; MATERIAL FATIGUE; SKEW-ELLIPTICAL DISTRIBUTIONS;

FATIGUE OF MATERIALS;

EID: 32444438104     PISSN: 03610926     EISSN: None     Source Type: Journal    
DOI: 10.1080/03610920500440065     Document Type: Article

References (29)

1. Arellano-Valle, R., Del Pino, G., San Martín, E. (2002). Definition and probabilistic properties of skew distributions. Statist. Prob. Letters 58:111-112.
2. Arellano-Valle, R. B., Gómez, H. W., Quintana, F. A. (2004). A new class of skew-normal distributions. Commun. Statist. Theor. Meth. 33(7): 1465-1480.
3. Azzalini, A. (1985). A class of distributions which includes the normal ones. Scand. J. Statist. 12:171-178.
4. Azzalini, A., Dalla Valle, A. (1996). The multivariate skew-normal distribution. Biometrika 83:715-726.
5. Azzalini, A., Capitanio, A. (1999). Statistical applications of the multivariate skew-normal distribution. J. R. Statist. Soc. B 61:579-602.
6. Birnbaum, Z. W., Saunders, S. C. (1969). A new family of life distributions. J. Appl. Prob. 6:637-52.
7. Branco, M. D., Dey, D. K. (2001). A general class of multivariate skew-elliptical distributions. J. Multivar. Anal. 79(1):99-113.
8. Chang, D. S., Tang, L. C. (1994). Percentile bounds and tolerance limits for the Birnbaum-Saunders distribution. Commun. Statist. Theor. Meth. 23:2853-2863.
9. Desmond, A. (1985). Stochastic models of failure in random environments. Canad. J. Statist. 13:171-183.
10. Díaz-García, J. A., Leiva-Sánchez, V. (2003). Doubly non-central t and script F sign distributions obtained under singular and non-singular elliptic distributions. Commun. Statist. Theor. Meth. 32(1): 11-32.
11. Díaz-García, J. A., Leiva-Sánchez, V. (2005). A new family of life distributions based on the contoured elliptically distributions. J. Statist. Plann. Infer. 128(2):445-457.
12. Díaz-García, J. A., Leiva-Sánchez, V., Galea, M. (2002). Singular elliptic distribution: density and applications. Commun. Statist. Theor. Meth. 31(5):665-681.
13. Fang, K. T., Zhang, Y. T. (1990). Generalized Multivariate Analysis. Beijing: Sciences Press, Berlin: Springer-Verlag.
14. Fang, K. T., Kotz, S., Ng, K. W. (1990). Symmetric Multivariate and Related Distribution. London: Chapman and Hall.
15. Galea, M., Leiva-Sánchez, V., Paula, G. (2004). Influence diagnostics in log-Birnbaum-Saunders regression models. J. Appl. Statist. 31(9):1049-1064.
16. Genton, M. G. (2004). Skew-elliptical Distributions and Their Applications. New York: Chapman and Hall/CRC.
17. Gupta, A. K., Varga, T. (1993). Elliptically Contoured Models in Statistics. Boston: Kluwer Academic Publishers.
18. Gupta, A. K., Chang, F. C., Huang, W. J. (2002). Some skew-symmetric model. Random Operators Stochastic Eq. 10(2): 133-140.
19. Gupta, A. K., Farías-González, G., Domínguez-Molina, J. A. (2004). A multivariate skew normal distributions. J. Multivar. Anal. 89:181-190.
20. Jeng, S. L. (2003). Inferences for the fatigue life model based on the Birnbaum-Saunders distribution. Commun. Statist. Simul. Comp. 32(1):43-60.
21. Johnson, N. L., Kotz, S., Kemp, A. (1993). Univariate Discrete Distributions. New York: Wiley & Sons.
22. Johnson, N. L., Kotz, S., Balakrishnan, N. (1995). Continuous Univariate Distributions. Vol. 2. New York: Wiley & Sons.
23. Meeker, W. Q., Escobar, L. A. (1998). Statistical Methods for Reliability Data. New York: John Wiley & Sons.
24. Murthy, V. K. (1974). The General Point Process: Applications to Structural Fatigue, Bioscience, and Medical Research. Addison-Wesley Publishing Company.
25. Ng, H. K., Kundu, D., Balakrishnan, N. (2003). Modified moment estimation for the two-parameter Birnbaum-Saunders distribution. Comp. Statist. Data Anal. 43:283-298.
26. Saunders, S. C. (1974). A family of random variables closed under reciprocation. J. Amer. Statist. Soc. 6:319-327.
27. Saunders, S. C. (1976). The problems of estimating a fatigue service life with a low probability of failure. Eng. Fracture Mechan. 8:205-215.
28. Subbotin, M. (1923). On the law frequency of errors. Mathematicheskii Sbornik 31:296-301.
29. Valluri, R. S. (1963). Some recent developments at galci concerning a theory of metal fatigue. Acta Metallurgica 11:759-775.