Distribución Bivariada Birnbaum-Saunders Unitaria

dc.contributorVergara Cardozo, Sandra
dc.contributorMartínez Flórez, Guillermo
dc.creatorRodríguez Quevedo, Luisa Paulina
dc.date.accessioned2023-04-24T21:37:03Z
dc.date.accessioned2023-06-06T22:37:15Z
dc.date.available2023-04-24T21:37:03Z
dc.date.available2023-06-06T22:37:15Z
dc.date.created2023-04-24T21:37:03Z
dc.date.issued2023
dc.identifierhttps://repositorio.unal.edu.co/handle/unal/83771
dc.identifierUniversidad Nacional de Colombia
dc.identifierRepositorio Institucional Universidad Nacional de Colombia
dc.identifierhttps://repositorio.unal.edu.co/
dc.identifier.urihttps://repositorioslatinoamericanos.uchile.cl/handle/2250/6650795
dc.description.abstractLa distribución Unitaria Birnbaum Saunders (UBS), [Mazucheli et al., 2018a], tiene soporte en el intervalo (0,1), motivo por el cual se emplea con éxito en el modelamiento de tasas e indicadores. Se presentan dos nuevas distribuciones bivariadas, la distribución Bivariada Birnbaum Saunders Unitaria (BVUBS) y la distribución Bivariada Sinh-Normal Birnbaum Saunders Unitaria (BVUSHN), además como efecto natural el modelo de regresión para el caso de covariables en el modelo, empleando para ello el concepto de distribuciones condicionalmente especificadas, dichas distribuciones son capaces de modelar tasas y proporciones en el plano unidad, y presentan un mejor ajuste a datos comparadas con otras distribuciones. Igualmente, se presentan algunas propiedades generales de los modelos, valores esperados e inferencia por máxima verosimilitud y aplicación a datos reales. Conjuntamente al presente trabajo de maestría se publica el artículo The Multivariate Skewed Log-Birnbaum–Saunders Distribution and Its Associated Regression Model, [Martínez-Flórez et al., 2023], el cual se enfocó en la extensión multivariada de la distribución Sinh-Normal Unitaria, estudiando en detalle las propiedades de la distribución e inferencia estadística, se incluye un estudio de simulación asociado al modelo de regresión y dos aplicaciones con datos reales, logrando concluir que son potencialmente útiles para modelar datos de proporciones, tasas o índices. (Texto tomado de la fuente)
dc.description.abstractThe unit-Birnbaum-Saunders distribution (UBS), [Mazucheli et al., 2018a], has support in the interval (0,1), which is why it is used successfully in the modeling of rates and indicators. Two new bivariate distributions are presented, the Bivariate Unit-Birnbaum-Saunders distribution (BVUBS) and the Bivariate Unit-Sinh-Normal Birnbaum Saunders distribution (BVUSHN), as well as the natural effect the regression model for the case of covariates in the model, using the concept of conditionally specified distributions, these distributions are capable of modeling rates and proportions in the unit plane, and present a better fit to data compared to other distributions. Likewise, some general properties of the models, expected values and inference by maximum likelihood and application to real data are presented. The article The Multivariate Skewed Log-Birnbaum–Saunders Distribution and Its Associated Regression Model, [Martínez-Flórez et al., 2023], which focused on the multivariate extension of the Unit-Sinh-Normal Distribution, is published together with this master's thesis, studying in detail the properties of the distribution and statistical inference, a simulation study associated with the regression model and two applications with real data are included. We conclude that they are potentially useful for modeling ratio, rate or index data.
dc.languagespa
dc.publisherUniversidad Nacional de Colombia
dc.publisherBogotá - Ciencias - Maestría en Ciencias - Estadística
dc.publisherFacultad de Ciencias
dc.publisherBogotá,Colombia
dc.publisherUniversidad Nacional de Colombia - Sede Bogotá
dc.relationAhmed, S., Castro-Kuriss, C., Leiva, V., Flores, E., and Sanhueza, A. (2010). Truncated version of the birnbaum–saunders distribution with an application in financial risk. Pakistan Journal of Statistics, 26:293–311
dc.relationArnold, B., Castillo, E., and Sarabia, J. (2002). Conditionally specified multivariate skewed distributions. The Indian Journal of Statistics, 64(2):206–226. http: //www.jstor.org/stable/25051391
dc.relationAthayde, E. (2017). A characterization of the birnbaum–saunders distribution. REVSTAT Statistical Journal, 15:333–354
dc.relationAzzalini, A. (1985). A class of distributions which includes the normal ones. Scandinavian Journal of Statistics, 12(2):171–178. http://www.jstor.org/stable/ 4615982
dc.relationBarlow, R. and Proschan, F. (1965). Mathematical theory of reliability. Wiley, 1
dc.relationBarros, M., Galea, M., Gonzalez, M., and Leiva, V. (2010). Infuence diagnostics in the tobit censored response model. Stat. Methods Appl., 19:379–397. https: //doi.org/10.1007/s10260-010-0135-y
dc.relationBartlett, M. and Kendall, D. (1946). The statistical analysis of variance-heterogeneity and the logarithmic transformation. Journal of the Royal Statistical Society: Series B, 8(1):128–138. https://doi.org/10.2307/2983618
dc.relationBebbington, M., Lai, C., and Zitikis, R. (2008). A proof of the shape of the birnbaum–saunders hazard rate function. Mathematical Scientist, 33:49–56
dc.relationBirnbaum, Z., Esary, J., and Marshall, A. (1966). Stochastic characterization of wear-out for components and systems. Annals of Mathematical Statistics, 37:816–825. https://www.jstor.org/stable/2238571
dc.relationBirnbaum, Z. W. and Saunders, S. (1969). A new family of life distributions. Journal of Applied Probability, 6(2):319–327. https://doi.org/10. 2307/3212003
dc.relationCepeda Cuervo, E., Achcar, J., and Garrido Lopera, B. (2014). Bivariate beta regression models: Joint modeling of the mean, dispersion and association parameters. Journal of Applied Statistics, 41. https://doi.org/10.1080/02664763. 2013.847071
dc.relationChhikara, R. and Folks, J. (1977). The inverse gaussian distribution as a lifetime model. Technometrics, 19(4):461–468. https://doi.org/10.2307/ 1267886
dc.relationCook, D., Kieschnick, R., and McCullough, B. (2008). Regression analysis of proportions in finance with self selection. Journal of Empirical Finance, 15:860–867. https://doi.org/10.1016/j.jempfin.2008.02.001
dc.relationDesmond, A. (1985). Stochastic models of failure in random environments. Statistical Society of Canada, 13(3):171–183. https://doi.org/10.2307/3315148
dc.relationDavis, J. (1952). An analysis of some failure data. Journal of the American Statistical Association, 47:113–150. https://doi.org/10.2307/2280740
dc.relationDupuis, D. and Mills, J. (1998). Robust estimation of the birnbaum-saunders distribution. IEEE Transactions on Reliability, 47:88–95
dc.relationEsary, J. and Marshall, A. (1973). Shock models and wear processes. The Annals of Probability, 1:627–649. https://www.jstor.org/stable/2959434
dc.relationFarias, R. and Lemonte, A. (2011). Bayesian inference for the birnbaum–saunders nonlinear regression model. Statistical Methods and Applications, 20:423–438. https://doi.org/10.1007/s10260-011-0165-0
dc.relationDíaz, J. and Leiva, V. (2005). A new family of life distributions based on the elliptically contoured distributions. Journal of Statistical Planning and Inference, 128:445–457. https://www.sciencedirect.com/science/article/pii/ S0378375804000072
dc.relationDíaz-García, J. and Domínguez-Molina, J. (2006). Some generalisations of birnbaum–saunders and sinh-normal distributions. International Mathematical Forum, 1:1709–1727. http://dx.doi.org/10.12988/imf.2006. 06146
dc.relationFreeman, D. (2007). Drunk driving legislation and traffic fatalities: New evidence on bac 08 laws. Contemporary Economic Policy 25, 293–308
dc.relationFreudenthal, A. and Shinozuka, M. (1961). Structural Safety Under Conditions of Ultimate Load Failure and Fatigue. Wright Air Development Division
dc.relationGalea, M., Leiva, V., and Paula, G. (2004). Influence diagnostics in log-birnbaum–saunders regression models. Journal of Applied Statistics, 31:1049–1064. https://doi.org/10.1080/0266476042000280409
dc.relationGarcia, F., Uribe, M., Leiva, V., and Aykroyd, G. (2017). Birnbaumsaunders spatial modelling and diagnostics applied to agricultural engineering data. Stochastic Environmental Research and Risk Assessment, 31:105–124. https://doi.org/ 10.1007/s00477-015-1204-4
dc.relationGuiraud, P., Leiva, V., and Fierro, R. (2009). A non-central version of the birnbaum–saunders distribution for reliability analysis. IEEE Transactions on Reliability., 58:152–160. https://ieeexplore.ieee.org/document/4781589
dc.relationGupta, A. and Nadarajah, S. (2004). Handbook of Beta Distribution and Applications. CRC Press
dc.relationKumaraswamy, P. (1980). A generalized probability density function for double-bounded random processes. Journal of Hydrology, 46:79–88. https://doi. org/10.1016/0022-1694(80)90036-0
dc.relationKundu, D. (2015). Bivariate log-birnbaum-saunders distribution. Statistics, 49:900–917. https://doi.org/10.1080/02331888.2014.915840
dc.relationKundu, D., N. Balakrishnan, B., and Jamalizadeh, A. (2010). Bivariate birnbaum–saunders distribution and associated inference. Journal of Multivariate Analysis, 101:113–125. https://doi.org/10.1016/j.jmva.2009.05.005
dc.relationKundu, D., Narayanaswamy, B., and Jamalizadeh, A. (2013). Generalized multivariate birnbaum–saunders distributions and related inferential issues. Journal of Multivariate Analysis, 40:230–244. https://doi.org/10.1016/j.jmva.2012.10.017
dc.relationLeiva, V. (2016). The Birnbaum Saunders distribution, volume 1. Elsevier
dc.relationLeiva, V., Riquelme, M., Balakrishnan, N., and Sanhueza, A. (2006). A new fatigue life model based on the family of skew-elliptical distributions. Stat. Theory Methods, 35:229–244
dc.relationLeiva, V., Riquelme, M., Balakrishnan, N., and Sanhueza, A. (2008). Lifetime analysis based on the generalized birnbaum–saunders distribution. Computational Statistics Data Analysis, 52:2079–2097. https://doi.org/10.1016/j.csda.2007.07. 003
dc.relationLeiva, V., Soto, G., Cabrera, E., and Cabrera, G. (2011). Nuevas cartas de control basadas en la distribución Birnbaum-Saunders y su implementación. Revista Colombiana de Estadística, 34:147–176
dc.relationLeiva, V., Vilca-Labra, F., Balakrishnan, N., and Sanhueza, A. (2010). A skewed sinh-normal distribution and its properties and application to air pollution. Communications in Statistics - Theory and Methods, 39:426–443. https://doi.org/10. 1080/03610920903140171
dc.relationLemonte, A. (2013). Multivariate birnbaum–saunders regression model. Journal of Statistical Computation and Simulation, 83(12):2244–2257. https://doi.org/ 10.1080/00949655.2012.688054
dc.relationLemonte, A. (2016). A note on the fisher information matrix of the birnbaum– saunders distribution. Journal of Statistical Theory and Applications, 15:196–205. https://doi.org/10.2991/jsta.2016.15.2.9
dc.relationLemonte, A. and Moreno-Arenas, G. (2019). On a multivariate regression model for rates and proportions. Journal of Applied Statistics, 46:1084–1106. https://doi.org/10.1080/02664763.2018.1534945
dc.relationLemonte, A. J. (2012). A log- birnbaum saunders regression model with asymmetric errors. Journal of Statistical Computation and Simulation, 82:1775–1787. https://doi.org/10.1080/00949655.2011.595715
dc.relationLieblein, J. (1956). Statistical investigation of the fatigue life of deep ball bearing. Journal of National Bureau of Standards, 57:273–316
dc.relationMartínez-Flórez, G. and Tovar-Falón, R. (2021). New regression models based on the unit-sinh-normal distributions: Properties, inference, and applications. Mathematics, 9(11), 1231. https://doi.org/10.3390/math9111231
dc.relationMartínez-Flórez, G., Azevedo, R., and Moreno-Arenas, G. (2017). Multivariate log-birnbaum–saunders regression models. Communications in Statistics - Theory and Methods, 46:10166–10178. https://doi.org/10.1080/03610926. 2016.1231818
dc.relationMazucheli, J., Leiva, V., Alves, B., and Menezes, A. (2021). A new quantile regression for modeling bounded data under a unit birnbaum- saunders distribution with aplplications in medicine and politics. Symmetry, 13(4):682. https: //doi.org/10.3390/sym13040682
dc.relationMartínez-Flórez, G., Vergara-Cardozo, S., Tovar-Falón, R., and Rodriguez-Quevedo, L. (2023). The multivariate skewed log-birnbaum saunders distribution and its associated regression model. Mathematics, 11(5), 1095. http: //dx.doi.org/10.3390/math11051095
dc.relationMazucheli, J., Menezes, A., and Dey, S. (2018a). The unit birnbaum- saunders distribution with applications. Chilean Journal of Statistics, 9:47– 57
dc.relationMazucheli, J., Menezes, F., and Ghitany, M. (2018b). The unit weibull distribution and associated inference. Journal of Applied Probability and Statistics, 13:1–22
dc.relationMiner, M. (1945). Cumulative damage in fatigue. Journal of Applied Mechanics, 12(3):A159–A164. https://doi.org/10.1115/1.4009458
dc.relationNelson, W. and Hahn, G. (1972). Linear estimation of a regression relationships from censored data, part i-simple methods and their applications. Technometrics, 14:247–269. https://doi.org/10.1080/00401706.1972.10488912
dc.relationOrtega, E., Bolfarine, H., and Paula, G. (2003). Infuence diagnostics in generalized log-gamma regression models. Computational Statistics Data Analysis, 42:165–186. https://doi.org/10.1016/S0167-9473(02)00104-4
dc.relationOwen, W. and Padgett, W. (1999). Accelerated test models for system strength based on birnbaum–saunders distribution. Lifetime Data Analysis, 5(2):133–147. https://doi.org/10.1023/A:1009649428243
dc.relationR Core Team (2022). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. https://www. R-project.org/
dc.relationRieck, J. and Nedelman, J. (1991). A log-linear model for the birnbaum–saunders distribution. Technometrics, 33(1):51–60. https://doi.org/ 10.2307/1269007
dc.relationShea, J. and Brown, K. (2022). Wooldridge: 115 data sets. In Introductory Econometrics: A Modern Approach, 7e, R package version 1.4-2
dc.relationVilca, F., Narayanaswamy, B., and C., B. (2014). A robust extension of the bivariate birnbaum–saunders distribution and associated inference. Journal of Multivariate Analysis, 35:418–435. https://doi.org/10.1016/j.jmva.2013.11.005
dc.relationVolodin, I. and Dzhungurova, O. (2000). On limit distribution emerging in the generalized birnbaum–saunders model. Journal of Mathematical Science, 99:1348–66. https://doi.org/10.1007/BF02674095
dc.relationXie, F. and Wei, B. (2007). Diagnostics analysis for logbirnbaum– saunders regression models. Computational Statistics y Data Analysis, 51:4692– 4706. https://doi.org/10.1016/j.csda.2006.08.030
dc.relationZelen, M. and Dannemiller, M. (1961). The robustness of life testing procedures derived from the exponential distribution. Technometrics, 3(1):29–49. https://doi.org/10.2307/1266475
dc.relationLemonte, A., Martínez-Florez, G., and Moreno-Arenas, G. (2015b). Multivariate birnbaum–saunders distribution: Properties and associated inference. Journal of Statistical Computation and Simulation, 85:374–392. https://doi.org/10.1080/ 00949655.2013.823964
dc.relationLemonte, A., Martínez, G., and Moreno-Arenas, G. (2015a). Multivariate birnbaum–saunders distribution: properties and associated inference. Journal of Statistical Computation and Simulation, 1:374–392. https://doi.org/10.1080/ 00949655.2013.823964
dc.relationMartínez-Flórez, G., Bolfarine, H., and Gómez, H. (2015). Doubly censored power-normal regression models with inflation. Journal of Theoretical and Applied Statistics, 24:265–286. https://doi.org/10.1007/s11749-014-0406-2
dc.relationKao, J. (1959). A graphical estimation of mixed weibull parameters in life-testing of electron tubes. Technometrics, 1:389–407. https://doi.org/10.2307/1266719
dc.rightsAtribución-NoComercial-SinDerivadas 4.0 Internacional
dc.rightshttp://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rightsinfo:eu-repo/semantics/openAccess
dc.titleDistribución Bivariada Birnbaum-Saunders Unitaria
dc.typeTrabajo de grado - Maestría


Este ítem pertenece a la siguiente institución