References
- Ahmed, S. E., Castro-Kuriss, C., Flores, E., Leiva, V., and Sanhueza, A. 2010. A truncated version of the Birnbaum–Saunders distribution with an application in financial risk. Pak. J. Stat., 26(1), 293–311.
- Ahmed, S. E., Budsaba, K., Lisawadi, S., and Volodin, A. I. 2008. Parametric estimation for the Birnbaum–Saunders lifetime distribution based on a new parameterization. Thailand Statistician, 6, 213–240.
- Apostol, T. M. 1969. Calculus, vol II, 2nd ed. New York, NY: John Wiley & Sons.
- Arnold, B. C., and Beaver, R. J. 2002. Skewed multivariate models related to hidden truncation and/or selective reporting. Test, 11(1), 7–54.
- Azzalini, A. 1985. A class of distributions which include the normal. Scand. J. Stat., 12, 171–178.
- Bhattacharyya, G. K., and Fries, A. 1980. Fatigue failure models—Birnbaum–Saunders vs. inverse Gaussian. IEEE Trans. Reliability, R-31, 439–440.
- Birnbaum, Z. W., and Saunders, S. C. 1969a. A new family of life distribution. J. Appl. Probability, 6, 319–327.
- Birnbaum, Z. W., and Saunders, S. C. 1969b. Estimation for a family of life distribuitions with applications to fatigue. J. Appl. Probability, 6, 328–347.
- Caro-Lopera, F. J., Leiva, V., and Balakrishnan, N. 2012. Connection between the Hadamard and matrix products with an application to matrix-variate Birnbaum–Saunders distributions. J. Multivariate Anal., 104, 126–139.
- Cordeiro, G. M., and Lemonte, A. J. 2011. The Birnbaum–Saunders distribution: An improved distribution for fatigue life modeling. Comput. Stat. Data Anal., 55, 1445–1461.
- Desmond, A. F. 1985. Stochastic models of failure in random environments. Can. J. Stat., 13(2), 171–183.
- Desmond, A. F. 1986. On the relationship between two fatigue-life models. IEEE Trans. Reliability, 35(2), 167–169.
- Diaz-García, J. A., and Domínguez-Molina, J. R. 2007. A new family of life distributions for dependent data: Estimation, Comput. Stat. Data Anal., 51, 5927–5939.
- Díaz-García, J. A., and Leiva, V. 2005. A new family of life distributions based on elliptically contoured distributions. J. Stat. Plan. Inference, 128(2), 445–457.
- Fletcher, H. 1911. A verification of the theory of Brownian movements and a direct determination of the value of NE for gaseous ionization. Phys. Rev., 33, 81–110.
- Ghodrat, S. 2013. Thermo-mechanical fatigue of compacted graphite iron in diesel engine components. PhD thesis, Delft University of Technology, Delft, The Netherlands.
- Glaser, R. A. 1980. Bathtub and related failure rate characterization. J. Am. Stat. Assoc., 75, 667–672.
- Gómez, H. W., Olivares-Pacheco, J. F., and Bolfarine, H. 2009. An extension of the generalized Birnbaum–Saunders distribution. Stat. Prob. Lett., 79, 331–338.
- Gundlach, R. B. 1983. The effect of alloying elements on the elevated temperature properties of gray irons. Trans. Am. Foundrymen’s Soc., 91, 389–422.
- Gupta, R. C., and Gupta, R. D. 2004. Generalized skew normal model. Test, 13(2), 501–524.
- Konstantinowsky, D. 1914. Elektrische ladungen and Brown’sche bewegung sehr kleiner metallteilchen in Gasen. Sitzungsberitcder Kaiserlichen Akademie der Wissenschften, 123, 1697–1752.
- Kundu, D., Kannan, N., and Balakrishnan, N. 2008. On the hazard function of Birnbaum–Saunders distribution and associated inference. Comput. Stat. Data Anal., 52, 2692–2702.
- Kundu, D., Balakrishnan, N., and Jamalizadeh, A. 2010. Bivariate Birnbaum–Saunders distribution and associated inference. J. Multivariate Anal., 101, 113–125.
- Kundu, D., Balakrishnan, N., and Jamalizadeh, A. 2013. Generalized multivariate Birnbaum–Saunders distribution and related inferential issues. J. Multivariate Anal., 116, 230–244.
- Leiva, V., Sanhueza, A., and Angulo, J. M. 2009. A length-biased version of the Birnbaum–Saunders distribution with application in water quality. Stochastic Environ. Res. Risk Assess., 23, 299–307.
- Lemonte, A. J., Cribari-Neto, F., and Vasconcellos, K. L. P. 2007. Improved statistical inference for the two-parameter Birnbaum–Saunders distribution. Comput. Stat. Data Anal., 51, 4656–4681.
- Liu, J. H., Hao, X. Y., Li, G. L., and Liu. G. S. 2002. Microvoid evaluation of ferrite ductile iron under strain. Mater. Lett., 56, 748–755.
- Mann, N. R., Schafer, R. E., and Singpurwalla, N. D. 1974. Methods for statistical analysis of reliability and life data. New York, NY: John Wiley & Sons.
- Mittelhammer, R. C., Judge, G. G., and Miller, D. J. 2000. Econometric foundations. New York, NY: Cambridge University Press.
- Ng, H. K. T., Kundu, D., and Balakrishnan, N. 2003. Modified moment estimation for the two-parameter Birnbaum–Saunders distribution. Comput. Stat. Data Anal., 43, 283–298.
- Owen, W. J. 2006. A new three parameter extension to the Birnbaum–Saunders distribution. IEEE Trans. Reliability, 55, 475–479.
- Rundman, K. B. 2001. Cast irons. In Encyclpedia of materials: Science and technology, 1003–1010. New York, NY: Elsevier.
- Santos-Neto, M., Cysneiros, F. J. A., Leiva, A., and Ahmed, S. E. 2012. On new parameterizations of the Birnbaum–Saunders distribution. Pak. J. Stat., 28(1), 1–26.
- Self, S. G., and Liang, K. 1987. Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions. J. Am. Stat. Assoc., 82(398), 605–610.
- Vilca, F., and Leiva, V. 2006. A new fatigue life model based on the family of skew-elliptic distributions. Commun. Stat. Theory Methods, 35, 229–244.