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.
@article{bwmeta1.element.doi-10_2478_bile-2013-0006, author = {M. Ivette Gomes and Marta Ferreira and V\'\i ctor Leiva}, title = {The extreme value Birnbaum-Saunders model, its moments and an application in biometry}, journal = {Biometrical Letters}, volume = {49}, year = {2012}, pages = {81-94}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_bile-2013-0006} }
M. Ivette Gomes; Marta Ferreira; Víctor Leiva. The extreme value Birnbaum-Saunders model, its moments and an application in biometry. Biometrical Letters, Tome 49 (2012) pp. 81-94. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_bile-2013-0006/
Abramowitz M., Stegun I.A. (1972): Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover, New York. | Zbl 0543.33001
Birnbaum Z.W., Saunders S.C. (1969): A new family of life distributions. J. Applied Probab. 6: 319-327. | Zbl 0209.49801
Ferreira M., Gomes M.I., Leiva V. (2012): On an Extreme Value Version of the Birnbaum-Saunders Distribution. Revstat (in press). | Zbl 1297.60006
Fréchet M. (1927): Sur la loi de probabilité de l'écart maximum. Ann. Société Polonaise de Mathématique 6: 93-116. | Zbl 54.0562.06
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. | Zbl 54.0560.05
Gnedenko B.V. (1943): Sur la distribution limite du terme maximum d'une série aléatoire. Ann. Math. 44: 423-453. | Zbl 0063.01643
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 | Zbl 1164.62014
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. | Zbl 05560064
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. | Zbl 1136.62016
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. | Zbl 1084.62107