222
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

An extended Birnbaum–Saunders distribution: Theory, estimation, and applications

, , , , &
Pages 2268-2297 | Received 12 Jul 2013, Accepted 23 Dec 2013, Published online: 30 Mar 2016

References

  • Barakat, H.M., Abdelkader, Y.H. (2004). Computing the moments of order statistics from nonidentical random variables. Stat. Methods Appl. 13:13–24.
  • Birnbaum, Z.W., Saunders, S.C. (1969a). A new family of life distributions. J. Appl. Probab. 6:319–327.
  • Birnbaum, Z.W., Saunders, S.C. (1969b). Estimation for a family of life distributions with applications to fatigue. J. Appl. Probab. 6:328–377.
  • Cordeiro, G.M., Lemonte, A.J. (2011). The beta Birnbaum–Saunders distribution: an improved distribution for fatigue life modeling. Comput. Stat. Data Anal. 55:1445–1461.
  • Cordeiro, G.M., Lemonte, A.J., Ortega, E.M.M. (2011a). An extended fatigue life distribution. Statistics. doi:10.1080/02331888.2011.617447
  • Cordeiro, G.M., Ortega, E.M.M., Silva, G.O. (2011b). The exponentiated generalized gamma distribution with application to lifetime data. J. Stat. Comput. Simul. 81:827–842.
  • Cowles, M.K., Carlin, B.P. (1996). Markov chain Monte Carlo convergence diagnostics: a comparative review. J. Am. Stat. Assoc. 91:133–169.
  • Díaz-García, J.A., Leiva, V. (2005). A new family of life distributions based on elliptically contoured distributions. J. Stat. Plan. Infer. 137:1512–1513.
  • Fleming, T.R., O’Fallon, J.R., O’Brien, P.C., Harrington, D.P. (1980). Modified Kolmogorov–Smirnov test procedures with application to arbitrarily right censored data. Biometrics 36:607–626.
  • Gelman, A., Rubin, D.B. (1992). Inference from iterative simulation using multiple sequences (with discussion). Stat. Sci. 7:457–472.
  • Gradshteyn, I.S., Ryzhik, I.M. (2007). Table of Integrals, Series, and Products. New York: Academic Press.
  • Greenwood, J.A., Landwehr, J.M., Matalas, N.C., Wallis, J.R. (1979). Probability weighted moments: definition and relation to parameters of several distributions expressible in inverse form. Water Resour. Res. 15:1049–1054.
  • Guiraud, P., Leiva, V., Fierro, R. (2009). A non-central version of the Birnbaum–Saunders distribution for reliability analysis. IEEE Trans. Reliab. 58:152–160.
  • Gupta, R.C., Gupta, P.L., Gupta, R.D. (1998). Modeling failure time data by Lehman alternatives. Commun. Stat. Theory Methods. 27:887–904.
  • Gupta, R.D., Kundu, D. (2001). Exponentiated exponential family: an alternative to gamma and Weibull distributions. Biom. J. 43:117–130.
  • Harris, F.E. (2008). Incomplete Bessel, generalized incomplete gamma, or leaky aquifer functions. J. Comput. Appl. Math. 215:260–269.
  • Jones, D.S. (2007a). Incomplete Bessel functions. Proc. Edinburgh Math. Soc. 50:173–183.
  • Jones, D.S. (2007b). Incomplete Bessel functions. Asymptotic expansions for large argument. Proc. Edinburgh Math. Soc. 50:711–723.
  • Kundu, D., Kannan, N., Balakrishnan, N. (2008). On the function of Birnbaum-Saunders distribution and associated inference. Comput. Stat. Data Anal. 52:2692–2702.
  • Lemonte, A.J., Cribari-Neto, F., Vasconcellos, K.L.P. (2007). Improved statistical inference for the two-parameter Birnbaum-Saunders distribution. Comput. Stat. Data Anal. 51:4656–4681.
  • Lemonte, A.J., Simas, A.B., Cribari-Neto, F. (2008). Bootstrap-based improved estimators for the two-parameter Birnbaum-Saunders distribution. J. Stat. Comput. Simul. 78:37–49.
  • Mudholkar, G.S., Srivastava, D.K. (1993). Exponentiated Weibull family for analyzing bathtub failure-real data. IEEE Trans. Reliab. 42:299–302.
  • Mudholkar, G.S., Srivastava, D.K., Friemer, M. (1995). The exponential Weibull family: a reanalysis of the bus-motor failure data. Technometrics 37:436–445.
  • Murthy, D.N.P., Xie, M., Jiang, R. (2004). Weibull Models. Hoboken, NJ: John Wiley.
  • Nadarajah, S., Cordeiro, G.M., Ortega, E.M.M. (2015). The Zografos–Balakrishnan-G family of distributions: Mathematical properties and applications. Communication in Statistics-Theory and Methods 44:186–215.
  • Nadarajah, S., Gupta, A.K. (2007). A generalized gamma distribution with application to drought data. Math. Comput. Simul. 74:1–7.
  • Rieck, J.R., Nedelman, J.R. (1991). A log-linear model for the Birnbaum–Saunders distribution. Technometrics, 33:51–60.
  • Rieck, J.R. (1999). A moment-generating function with application to the Birnbaum-Saunders distribution. Commun. Stat. Theory Methods. 28:2213–2222.
  • Ristic, M.M., Balakrishnan, N. (2011). The gamma exponentiated exponential distribution. J. Stat. Comput. Simul. doi:10.1080/00949655.2011.574633
  • Terras, R. (1981). A Miller algorithm for an incomplete Bessel function. J. Comput. Phys. 39:233–240.
  • Watson, G.N. (1995). A Treatise on the Theory of Bessel Functions. United Kingdom: Cambridge University Press.
  • Wu, J., Wong, A.C.M. (2004). Improved interval estimation for the two-parameter Birnbaum-Saunders distribution. Comput. Stat. Data Anal. 47:809–821.
  • Zografos, K., Balakrishnan, N. (2009). On families of beta- and generalized gamma-generated distributions and associated inference. Stat. Method. 6:344–362.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.