The Birnbaum-Saunders (BS) model is a life distribution that has been widely studied and applied. Recently, a new version of the BS distribution based on extreme value theory has been introduced, named the extreme value Birnbaum-Saunders (EVBS) distribution. In this article we provide some further details on the EVBS models that can be useful as a supplement to the existing results. We use these models to analyse real survival time data for patients treated with alkylating agents for multiple myeloma. This analysis allow us to show the adequacy of these new statistical distributions and identify them as models useful for medical practitioners in order to predict survival times for such patients and evaluate changes in their treatment dose.
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Abramowitz M. Stegun I.A. (1972): Handbook of Mathematical Functions with Formulas Graphs and Mathematical Tables. Dover New York.
Birnbaum Z.W. Saunders S.C. (1969): A new family of life distributions. J. Applied Probab. 6: 319-327.
Ferreira M. Gomes M.I. Leiva V. (2012): On an Extreme Value Version of the Birnbaum-Saunders Distribution. Revstat (in press).
Fréchet M. (1927): Sur la loi de probabilité de l'écart maximum. Ann. Société Polonaise de Mathématique 6: 93-116.
Fisher R.A. Tippett L.H.C. (1928): Limiting forms of the frequency of the largest or smallest member of a sample. Proc. Cambridge Phil. Soc. 24: 180-190.
Gnedenko B.V. (1943): Sur la distribution limite du terme maximum d'une série aléatoire. Ann. Math. 44: 423-453.
Gomes M.I. Canto e Castro L. Fraga Alves M.I. Pestana D. (2008): Statistics of extremes for iid data and breakthroughs in the estimation of the extreme value index: Laurens de Haan leading contributions. Extremes 11(1): 3-34
Jenkinson A.F. (1955): The frequency distribution of the annual maximum (or minimum) values of meteorological elements. Quart. J. Royal Meteorol. Society 81: 158-171.
Leiva V. Barros M. Paula G.A. Galea M. (2007): Inuence diagnostics in log- Birnbaum-Saunders regression models with censored data. Comp. Stat. Data Anal. 51: 5694-5707.
Sanhueza A. Leiva V. Balakrishnan N. (2008): The generalized Birnbaum- Saunders distribution and its theory methodology and application. Comm. Statist. - Theory and Methods 37: 645-670.
Mises R. von (1936): La distribution de la plus grande de n valeurs. Revue Math. Union Interbalcanique 1 141-160.
Reprinted in Selected Papers of Richard von Mises. Amer. Math. Soc. 2(1964): 271-294.
Vilca F. Leiva V. (2006): A new fatigue life model based on the family of skewelliptical distributions. Comm. Statist. - Theory and Methods 35: 229-244.