Estimation of extreme percentiles in BirnbaumSaunders distributions

Computational Statistics and Data Analysis

Volumn 55, Issue 4, 2011, Pages 1665-1678

  Vilca, Filidor ^a   Santana, Lucia ^a   Leiva, Víctor ^b,c   Balakrishnan, N ^d  

^a UNIVERSITY OF CAMPINAS   (Brazil)

^b UNIVERSIDAD DE VALPARAÍSO   (Chile)

^c UNIVERSIDAD DE ANTOFAGASTA   (Chile)

^d MCMASTER UNIVERSITY   (Canada)

Author keywords

EM and ECM algorithms; Monte Carlo simulations; Skew distributions

Indexed keywords

BIRNBAUM-SAUNDERS DISTRIBUTION; DISTRIBUTION PARAMETERS; ECM ALGORITHM; EM ALGORITHMS; ENVIRONMENTAL DATA; ENVIRONMENTAL SCIENCE; LIKELIHOOD FUNCTIONS; MONTE CARLO SIMULATION; SIMULATION STUDIES; SKEW DISTRIBUTION; STATISTICAL LITERATURE;

ALGORITHMS; COMPUTER SIMULATION; MONTE CARLO METHODS;

MAXIMUM LIKELIHOOD ESTIMATION;

EID: 78650810913     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2010.10.023     Document Type: Article

References (41)

1. A.C. Atkinson Plots, Transformations and Regressions 1985 Oxford University Press Oxford
2. A. Azzalini A class of distributions which includes the normal ones Scand. J. Statist. 12 1985 171 178
3. A. Azzalini The skew-normal distribution and related multivariate families Scand. J. Statist. 32 2005 159 188
4. N. Balakrishnan, V. Leiva, A. Sanhueza, and F. Vilca Estimation in the BirnbaumSaunders distribution based on scale-mixture of normals and the EM algorithm Stat. Oper. Res. Trans. 33 2009 171 192
5. M. Barros, G.A. Paula, and V. Leiva A new class of survival regression models with heavy-tailed errors: robustness and diagnostics Lifetime Data Anal. 14 2008 316 332
6. Z.W. Birnbaum, and S.C. Saunders A probabilistic interpretation of Miner's rule SIAM J. Appl. Math. 16 1968 637 652
7. Z.W. Birnbaum, and S.C. Saunders A new family of life distributions J. Appl. Probab. 6 1969 319 327
8. Z.W. Birnbaum, and S.C. Saunders Estimation for a family of life distributions with applications to fatigue J. Appl. Probab. 6 1969 328 347
9. J.A. Daz-Garca, and V. Leiva A new family of life distributions based on elliptically contoured distributions J. Statist. Plann. Inference 128 2005 445 457 J. Statist. Plann. Inference137 15121513 (erratum)
10. A.P. Dempster, N.M. Laird, and D.B. Rubin Maximum likelihood from incomplete data via the EM algorithm J. R. Stat. Soc. B 39 1977 1 38
11. A. Desmond Stochastic models of failure in random environments Canad. J. Statist. 13 1985 171 183
12. K. Fang, S. Kotz, and K. Ng Symmetric Multivariate and Related Distributions 1990 Chapman & Hall London
13. M.G. Genton Skew-elliptical Distributions and Their Applications: A Journey Beyond Normality 2004 Chapman & Hall/CRC Press Boca Raton, FL
14. S. Gokhale, and M. Khare A review of deterministic, stochastic and hybrid vehicular exhaust emission models Int. J. Transp. Manag. 2 2004 59 74
15. S. Gokhale, and M. Khare Statistical behavior of carbon monoxide from vehicular exhausts in urban environments Environ. Model. Software 22 2007 526 535
16. H.W. Gomez, J. Olivares, and H. Bolfarine An extension of the generalized BirnbaumSaunders distribution Statist. Probab. Letters 79 2009 331 338
17. M. Hubert, and E. Vandervieren An adjusted boxplot for skewed distributions Comput. Statist. Data Anal. 52 2008 5186 5201
18. N.L. Johnson, S. Kotz, and N. Balakrishnan Second edition Continuous Univariate Distributions vol. 1 1994 John Wiley & Sons New York
19. N.L. Johnson, S. Kotz, and N. Balakrishnan Second edition Continuous Univariate Distributions vol. 2 1995 John Wiley & Sons New York
20. R.E. Kass, and A.E. Raftery Bayes factors J. Amer. Stat. Assoc. 90 1995 773 795
21. V. Leiva, M. Barros, G.A. Paula, and M. Galea Influence diagnostics in log-BirnbaumSaunders regression models with censored data Comput. Statist. Data Anal. 51 2007 5694 5707
22. V. Leiva, M. Barros, G. Paula, and D. Sanhueza Generalized BirnbaumSaunders distributions applied to air pollutant concentration Environmetrics 19 2008 235 249
23. V. Leiva, H. Hernndez, and M. Riquelme A new package for the BirnbaumSaunders distribution R Journal 6 2006 35 40 http://www.r-project.org/ doc/Rnews/Rnews2006-4.pdf
24. V. Leiva, M. Riquelme, N. Balakrishnan, and A. Sanhueza Lifetime analysis based on the generalized BirnbaumSaunders distribution Comput. Statist. Data Anal. 52 2008 2079 2097
25. V. Leiva, A. Sanhueza, and J.M. Angulo A length-biased version of the BirnbaumSaunders distribution with application in water quality Stoch. Environ. Res. Risk. Assess. 23 2009 299 307
26. V. Leiva, F. Vilca, N. Balakrishnan, and A. Sanhueza A skewed sinh-normal distribution and its properties and application to air pollution Comm. Statist. Theor. Meth. 39 2010 426 443
27. A.W. Marshall, and I. Olkin Life Distributions 2007 Springer New York
28. X.-L. Meng, and D.B. Rubin Maximum likelihood estimation via the ECM algorithm: a general framework Biometrika 80 1993 267 278
29. M.A. Miner Cumulative damage in fatigue J. Appl. Mech. 12 1945 159 164
30. S. Nadarajah A truncated inverted beta distribution with application to air pollution data Stoch. Environ. Res. Risk. Assess. 22 2008 285 289
31. H.K. Ng, D. Kundu, and N. Balakrisnan Modified moment estimation for the two-parameter BirnbaumSaunders distribution Comput. Statist. Data Anal. 43 2003 283 298
32. W.J. Owen, and W.J. Padgett A BirnbaumSaunders accelerated life model IEEE Trans. Rel. 49 2000 224 229
33. R. Podlaski Characterization of diameter data in near-natural forests using the BirnbaumSaunders distribution Can. J. For. Res. 38 2008 518 527
34. A.E. Raftery Bayesian model seletion in social research Sociol. Methods 25 1995 111 163
35. J.R. Rieck, and J.R. Nedelman A log-linear model for the BirnbaumSaunders distribution Technometrics 33 1991 51 60
36. A. Sanhueza, V. Leiva, and N. Balakrishnan The generalized Birnbaum-Saunders distribution and its theory, methodology and application Comm. Statist. Theor. Meth. 37 2008 645 670
37. Santana, L., Vilca, F., Leiva, V., 2011. Influence analysis in skew-BirnbaumSaunders regression models and applications. J. Appl. Stat. (in press). http://dx.doi.org/10.1080/02664763.2010.515679.
38. S.C. Saunders Reliability, Life Testing and Prediction of Services Lives 2007 Springer New York
39. D.J. Spiegelhalter, N.G. Best, B.P. Carlin, and A. van der Linde Bayesian measures of complexity and fit J. R. Stat. Soc. B 64 2002 1 34
40. F. Vilca, and V. Leiva A new fatigue life model based on family of skew-elliptical distributions Comm. Statist. Theor. Meth. 35 2006 229 244
41. F. Vilca, A. Sanhueza, V. Leiva, and G. Christakos An extended Birnbaum Saunders model and its application in the study of environmental quality in Santiago, Chile Stoch. Environ. Res. Risk. Assess. 24 2010 771 782