L-moments of the Birnbaum–Saunders distribution and its extreme value version: estimation, goodness of fit and application to earthquake data

References

• W.H. Asquith, Parameter estimation for the 4-parameter asymmetric exponential power distribution by the method of L-moments using R, Comput. Stat. Data Anal. 71 (2014), pp. 955–970. doi: 10.1016/j.csda.2012.12.013
   Web of Science ®Google Scholar
• M. Barros, V. Leiva, R. Ospina, and A. Tsuyuguchi, Goodness-of-fit tests for the Birnbaum–Saunders distribution with censored reliability data, IEEE Trans. Reliab. 63 (2014), pp. 543–554. doi: 10.1109/TR.2014.2313707
   Web of Science ®Google Scholar
• Z.W. Birnbaum and S.C. Saunders, Estimation for a family of life distributions with applications to fatigue, J. Appl. Probab. 6 (1969), pp. 328–347. doi: 10.1017/S002190020003285X
   Web of Science ®Google Scholar
• C. Castro-Kuriss, V. Leiva, and E. Athayde, Graphical tools to assess goodness-of-fit in non-location-scale distributions, Rev. Colombiana de Estadística 37 (2014), pp. 341–365. doi: 10.15446/rce.v37n2spe.47941
   Google Scholar
• S Coles, An Introduction to Statistical Modeling of Extreme Values, Springer, London, 2001.
   Google Scholar
• L. de Haan and A Ferreira, Extreme Value Theory: An Introduction, Springer, New York, 2006.
   Google Scholar
• P. Delicado and M.N. Goria, A small sample comparison of maximum likelihood, moments and L-moments methods for the asymmetric exponential power distribution, Comput. Stat. Data Anal. 52 (2008), pp. 1661–1673. doi: 10.1016/j.csda.2007.05.021
   Web of Science ®Google Scholar
• B. Efron, Censored data and the bootstrap, J. Amer. Stat. Assoc. 76 (1981), pp. 312–319. doi: 10.1080/01621459.1981.10477650
   Web of Science ®Google Scholar
• M. Ferreira, M.I. Gomes, and V. Leiva, On an extreme value version of the Birnbaum–Saunders distribution, REVSTAT Stat. J. 10 (2012), pp. 181–210.
   Web of Science ®Google Scholar
• R. Fierro and V. Leiva, A stochastic methodology for risk assessment of a large earthquake when a long time has elapsed, Stoch. Environ. Res. Risk Assess. (2016), pages in press available at http://dx.doi.org/10.1007/s00477–016–1288–5.
   PubMed Web of Science ®Google Scholar
• E.A. Flinn and E.R. Engdahl, A proposed basis for geographical and seismic regionalization, Rev. Geophys. 3 (1965), pp. 123–149. doi: 10.1029/RG003i001p00123
   Web of Science ®Google Scholar
• F. Garcia-Papani, M. Uribe-Opazo, V. Leiva, and R. Aykroyd, Birnbaum–Saunders spatial modelling and diagnostics applied to agricultural engineering data, Stoch. Environ. Res. Risk Assess. (2016), pages in press available at http://dx.doi.org/10.1007/s00477–015–1204–4.
   PubMed Web of Science ®Google Scholar
• J. Hosking and J Wallis, Regional Frequency Analysis: An Approach Based on L-moments, Cambridge Press, New York, 1997.
   Google Scholar
• N. Johnson, S. Kotz, and N Balakrishnan, Continuous Univariate Distributions, Vol. 2, Wiley, New York, 1995.
   Google Scholar
• Y.Y. Kagan, Seismic moment-frequency relation for shallow earthquakes: Regional comparison, J. Geophys. Res. 102 (1997), pp. 2835–2852. doi: 10.1029/96JB03386
   Web of Science ®Google Scholar
• A. Karakoca, U. Erisoglu, and M. Erisoglu, A comparison of the parameter estimation methods for bimodal mixture Weibull distribution with complete data, J. Appl. Stat. 42 (2015), pp. 1472–1489. doi: 10.1080/02664763.2014.1000275
   Web of Science ®Google Scholar
• J. Karvanen, Estimation of quantile mixtures via L-moments and trimmed L-moments, Comput. Stat. Data Anal. 51 (2006), pp. 947–959. doi: 10.1016/j.csda.2005.09.014
   Web of Science ®Google Scholar
• J. Karvanen, Lmoments: L-moments and quantile mixtures, 2016, R package version 1.2-3.
   Google Scholar
• D. Kim, B.J. Kim, S.-O. Lee, and Y.-S. Cho, Best-fit distribution and log-normality for tsunami heights along coastal lines, Stoch. Environ. Res. Risk Assess. 28 (2014), pp. 881–893. doi: 10.1007/s00477-013-0778-y
   Web of Science ®Google Scholar
• S. Kotz, V. Leiva, and A. Sanhueza, Two new mixture models related to the inverse Gaussian distribution, Methodol. Comput. Appl. Probab. 12 (2010), pp. 199–212. doi: 10.1007/s11009-008-9112-4
   Web of Science ®Google Scholar
• J. Kyselý and J. Picek, Regional growth curves and improved design value estimates of extreme precipitation events in the Czech Republic, Climate Res. 33 (2007), pp. 243–255. doi: 10.3354/cr033243
   Web of Science ®Google Scholar
• F. Laio, G. Baldassarre, and A. Montanari, Model selection techniques for the frequency analysis of hydrological extremes, Water Resour. Res. 45 (2009), pp. 1–11. doi: 10.1029/2008WR007292
   Web of Science ®Google Scholar
• J. Leao, V. Leiva, H. Saulo, and V. Tomazella, Birnbaum–Saunders frailty regression models: Diagnostics and application to medical data, Biometr. J. (2017), page in press available at http://dx.doi.org/10.1002/bimj.200800143.
   PubMed Web of Science ®Google Scholar
• V. Leiva, E. Athayde, C. Azevedo, and C. Marchant, Modeling wind energy flux by a Birnbaum–Saunders distribution with unknown shift parameter, J. Appl. Stat. 38 (2011), pp. 2819–2838. doi: 10.1080/02664763.2011.570319
   Web of Science ®Google Scholar
• V. Leiva, M. Barros, G.A. Paula, and A. Sanhueza, Generalized Birnbaum–Saunders distributions applied to air pollutant concentration, Environmetrics 19 (2008), pp. 235–249. doi: 10.1002/env.861
   Web of Science ®Google Scholar
• V. Leiva, M. Ferreira, M.I. Gomes, and C. Lillo, Extreme value Birnbaum–Saunders regression models applied to environmental data, Stoch. Environ. Res. Risk Assess. 30 (2016), pp. 1045–1058. doi: 10.1007/s00477-015-1069-6
   Web of Science ®Google Scholar
• V. Leiva, C. Marchant, F. Ruggeri, and H. Saulo, A criterion for environmental assessment using Birnbaum–Saunders attribute control charts, Environmetrics 26 (2015), pp. 463–476. doi: 10.1002/env.2349
   Web of Science ®Google Scholar
• V. Leiva, C. Marchant, H. Saulo, M. Aslam, and F. Rojas, Capability indices for Birnbaum–Saunders processes applied to electronic and food industries, J. Appl. Stat. 41 (2014), pp. 1881–1902. doi: 10.1080/02664763.2014.897690
   Web of Science ®Google Scholar
• V. Leiva, E. Rojas, M. Galea, and A. Sanhueza, Diagnostics in Birnbaum–Saunders accelerated life models with an application to fatigue data, Appl. Stoch. Models Bus. Ind. 30 (2014), pp. 115–131. doi: 10.1002/asmb.1944
   Web of Science ®Google Scholar
• V. Leiva, F. Ruggeri, H. Saulo, and J.F. Vivanco, A methodology based on the Birnbaum–Saunders distribution for reliability analysis applied to nano-materials, Reliab. Eng. Syst. Safety 157 (2017), pp. 192–201. doi: 10.1016/j.ress.2016.08.024
   Web of Science ®Google Scholar
• V. Leiva, A. Sanhueza, P.K. Sen, and G.A. Paula, Random number generators for the generalized Birnbaum–Saunders distribution, J. Stat. Comput. Simul. 78 (2008), pp. 1105–1118. doi: 10.1080/00949650701550242
   Web of Science ®Google Scholar
• V. Leiva, M. Santos-Neto, F.J.A. Cysneiros, and M. Barros, Birnbaum–Saunders statistical modelling: A new approach, Stat. Model. 14 (2014), pp. 21–48. doi: 10.1177/1471082X13494532
   Web of Science ®Google Scholar
• V. Leiva, M. Santos-Neto, F.J.A. Cysneiros, and M. Barros, A methodology for stochastic inventory models based on a zero-adjusted Birnbaum–Saunders distribution, Appl. Stoch. Models Bus. Ind. 32 (2016), pp. 74–89. doi: 10.1002/asmb.2124
   Web of Science ®Google Scholar
• V. Leiva and S.C. Saunders, Cumulative damage models, Wiley StatsRef: Statistics Reference. Online http://dx.doi.org/10.1002/9781118445112.stat02136.pub2, 2015, pp. 1–10.
   Google Scholar
• V. Leiva, M. Tejo, P. Guiraud, O. Schmachtenberg, P. Orio, and F. Marmolejo-Ramos, Modeling neural activity with cumulative damage distributions, Biol. Cybernet. 109 (2015), pp. 421–433. doi: 10.1007/s00422-015-0651-9
   PubMed Web of Science ®Google Scholar
• X. Li, Y. Zuo, X. Zhuang, and H. Zhu, Estimation of fracture trace length distributions using probability weighted moments and L-moments, Eng. Geol. 168 (2013), pp. 69–85. doi: 10.1016/j.enggeo.2013.10.025
   Web of Science ®Google Scholar
• J.-J. Liou, Y.-C. Wu, and K.-S. Cheng, Establishing acceptance regions for L-moments based goodness-of-fit tests by stochastic simulation, J. Hydrol. 355 (2008), pp. 49–62. doi: 10.1016/j.jhydrol.2008.02.023
   Web of Science ®Google Scholar
• C. Marchant, V. Leiva, M. Cavieres, and A. Sanhueza, Air contaminant statistical distributions with application to PM10 in Santiago, Chile, Rev. Environ. Contamination Toxicol. 223 (2013), pp. 1–31.
   PubMed Web of Science ®Google Scholar
• C. Marchant, V. Leiva, and F.J.A. Cysneiros, A multivariate log-linear model for Birnbaum–Saunders distributions, IEEE Trans. Reliab. 65 (2016), pp. 816–827. doi: 10.1109/TR.2015.2499964
   Web of Science ®Google Scholar
• C. Marchant, V. Leiva, F.J.A. Cysneiros, and J.F. Vivanco, Diagnostics in multivariate generalized Birnbaum–Saunders regression models, J. Appl. Stat. 43 (2016), pp. 2829–2849. doi: 10.1080/02664763.2016.1148671
   Web of Science ®Google Scholar
• O. Nicolis, M. Chiodi, and G. Adelfio, Windowed ETAS models with application to the Chilean seismic catalogs, Spatial Stat. 14 (2015), pp. 151–165. doi: 10.1016/j.spasta.2015.05.006
   Web of Science ®Google Scholar
• P. Rousseeuw, C. Croux, V. Todorov, A. Ruckstuhl, M. Salibian-Barrera, T. Verbeke, M. Koller, and M. Maechler, robustbase: Basic robust statistics, 2015, R package version 0.92-5.
   Google Scholar
• M. Santos-Neto, F.J.A. Cysneiros, V. Leiva, and M. Barros, Reparameterized Birnbaum–Saunders regression models with varying precision, Electron. J. Stat. 10 (2016), pp. 2825–2855. doi: 10.1214/16-EJS1187
   Web of Science ®Google Scholar
• H. Saulo, V. Leiva, F.A. Ziegelmann, and C. Marchant, A nonparametric method for estimating asymmetric densities based on skewed Birnbaum–Saunders distributions applied to environmental data, Stoch. Environ. Res. Risk Assess. 27 (2013), pp. 1479–1491. doi: 10.1007/s00477-012-0684-8
   Web of Science ®Google Scholar
• E. Thompson, L. Baise, and R. Vogel, A global index earthquake approach to probabilistic assessment of extremes, J. Geophys. Res. 112 (2007), pp. 1–12.
   Web of Science ®Google Scholar
• E.M. Thompson, J.B. Hewlett, L.G. Baise, and R.M. Vogel, The Gumbel hypothesis test for left censored observations using regional earthquake records as an example, Natur. Hazards Earth Syst. Sci. 11 (2011), pp. 115–126. doi: 10.5194/nhess-11-115-2011
   Web of Science ®Google Scholar
• T.J. Ulrych, D.R. Velis, A.D. Woodbury, and M.D. Sacchi, L-moments and C-moments, Stoch. Environ. Res. Risk Assess. 14 (2000), pp. 50–68. doi: 10.1007/s004770050004
   Web of Science ®Google Scholar
• N. Unnikrishnan Nair and B. Vineshkumar, L-moments of residual life, J. Statist. Plann. Inference 140 (2010), pp. 2618–2631. doi: 10.1016/j.jspi.2010.03.025
   Web of Science ®Google Scholar
• 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), pp. 771–782. doi: 10.1007/s00477-009-0363-6
   Web of Science ®Google Scholar
• R.M. Vogel, Recent advances and themes in hydrology, Rev. Geophys. 33 (1995), pp. 933–936. doi: 10.1029/95RG00935
   Web of Science ®Google Scholar
• D. Wang, A.D. Hutson, and J.C. Meicznikowsky, L-moment estimation for parametric survival models given censored data, Statist. Methodol. 7 (2014), pp. 655–667. doi: 10.1016/j.stamet.2010.07.002
   Google Scholar
• M. Wang, J. Zhao, X. Sun, and C. Park, Robust explicit estimation of the two-parameter Birnbaum–Saunders distribution, J. Appl. Stat. 40 (2013), pp. 2259–2274. doi: 10.1080/02664763.2013.809570
   Web of Science ®Google Scholar
• P. Wanke and V. Leiva, Exploring the potential use of the Birnbaum–Saunders distribution in inventory management, Math. Probl. Eng. (2015), pp. 1–9. Article ID 827246. doi: 10.1155/2015/827246
   Web of Science ®Google Scholar
• Y.-C. Wu, J.-J. Liou, Y.-F. Su, and K.-S. Cheng, Establishing acceptance regions for L-moments based goodness-of-fit tests for the Pearson type III distribution, Stoch. Environ. Res. Risk Assess. 26 (2012), pp. 873–885. doi: 10.1007/s00477-011-0519-z
   Web of Science ®Google Scholar