Contributions to the class of beta-generated distributions

References

• Akinsete, A., F. Famoye, and C. Lee. 2008. The beta-Pareto distribution. Statistics 42 (6):547–63. doi:10.1080/02331880801983876.
   Web of Science ®Google Scholar
• Alexander, C., G. M. Cordeiro, E. M. M. Ortega, and J. M. Sarabia. 2012. Generalized beta-generated distributions. Computational Statistics & Data Analysis 56 (6):1880–97. doi:10.1016/j.csda.2011.11.015.
   Web of Science ®Google Scholar
• Arnold, B. C., E. Castillo, and J. M. Sarabia. 1999. Conditional specification of statistical models. New York: Springer Verlag.
   Google Scholar
• Arnold, B. C., E. Castillo, and J. M. Sarabia. 2001. Conditionally specified distributions: An introduction (with discussion). Statistical Science 16:249–74.
   Web of Science ®Google Scholar
• Arnold, B. C., E. Castillo, and J. M. Sarabia. 2006. Families of multivariate distributions involving the Rosenblatt construction. Journal of the American Statistical Association 101 (476):1652–62. doi:10.1198/016214506000000159.
   Web of Science ®Google Scholar
• Barreto-Souza, W., A. H. S. Santos, and G. M. Cordeiro. 2010. The beta generalized-exponential distribution. Journal of Statistical Computation and Simulation 80 (2):159–72. doi:10.1080/00949650802552402.
   Web of Science ®Google Scholar
• Bustince, H., J. Fernandez, R. Mesiar, and T. Calvo. 2013. Aggregation functions in theory and in practise: Advances in intelligent systems and computing. Berlin, Heidelberg: Springer.
   Google Scholar
• Cont, R. 2001. Empirical properties of asset returns: Stylized facts and statistical issues. Journal of Computational Finance 1:223–36.
   Google Scholar
• Cordeiro, G. M., E. M. Ortega, and S. Nadarajah. 2010. The Kumaraswamy Weibull distribution with application to failure data. The Journal of the Franklin Institute 347 (8):1399–429. doi:10.1016/j.jfranklin.2010.06.010.
   Web of Science ®Google Scholar
• Engel, A. 1998. Problem-solving strategies: Problem books in mathematics. New York: Springer Verlag.
   Google Scholar
• Eugene, N., C. Lee, and F. Famoye. 2002. Beta-normal distribution and its applications. Communications in Statistics - Theory and Methods 31 (4):497–512. doi:10.1081/STA-120003130.
   Web of Science ®Google Scholar
• Famoye, F., and C. Lee, and N. Eugene. 2004. Beta-normal distribution: Bimodality properties and application. Journal of Modern Applied Statistical Methods 3 (1):85–103. doi:10.22237/jmasm/1083370200.
   Google Scholar
• Gradshteyn, I. S., and I. M. Ryzhik. 2007. Table of integrals, series and products. San Diego, CA: Academic Press.
   Google Scholar
• Jones, M. 2009. Kumaraswamy’s distribution: A beta-type distribution with some tractability advantages. Statistical Methodology 6 (1):70–81. doi:10.1016/j.stamet.2008.04.001.
   Google Scholar
• Jones, M. C. 2004. Families of distributions arising from distributions of order statistics. Test 13 (1):1–43. doi:10.1007/BF02602999.
   Web of Science ®Google Scholar
• Jones, M., and P. V. Larsen. 2004. Multivariate distributions with support above the diagonal. Biometrika 91 (4):975–86. doi:10.1093/biomet/91.4.975.
   Web of Science ®Google Scholar
• Kotz, S., Balakrishnan, N., and N. L. Johnson. 2000. Continuous multivariate distributions: Models and applications. Vol. 1. 2nd ed. New York: John Wiley & Sons, Inc.
   Google Scholar
• MATLAB. 2019. MATLAB (Release 2019). Natick, MA: The MathWorks, Inc.
   Google Scholar
• Nadarajah, S., G. M. Cordeiro, and E. M. M. Ortega. 2015. The Zografos-Balakrishnan-G family of distributions: Mathematical properties and applications. Communications in Statistics - Theory and Methods 44 (1):186–215. doi:10.1080/03610926.2012.740127.
   Web of Science ®Google Scholar
• Nadarajah, S., and A. Gupta. 2004. The beta-Fréchet distribution. Far East Journal of Theoretical Statistics 14:15–24.
   Google Scholar
• Nadarajah, S., and S. Kotz. 2004. The beta-Gumbel distribution. Mathematical Problems in engineering 10:323–32.
   Web of Science ®Google Scholar
• Nadarajah, S., and S. Kotz. 2006. The beta exponential distribution. Reliability Engineering & System Safety 91 (6):689–97. doi:10.1016/j.ress.2005.05.008.
   Web of Science ®Google Scholar
• Nadarajah, S., and R. Rocha. 2016a. Newdistns: An R package for new families of distributions. Journal of Statistical Software 69:1–32.
   Web of Science ®Google Scholar
• Nadarajah, S., and R. Rocha. 2016b. Newdistns: Computes PDF, CDF, quantile and random numbers, measures of inference for 19 general families of distributions. R package version 2.1.
   Google Scholar
• Nelder, J. A., and R. Mead. 1965. A simplex method for function minimization. The Computer Journal 7 (4):308–13. doi:10.1093/comjnl/7.4.308.
   Web of Science ®Google Scholar
• R Core Team. 2019. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria.
   Google Scholar
• Samanthi, R. G. M., and J. Sepanski. 2019. A bivariate extension of the beta generated distribution derived from copulas. Communications in Statistics - Theory and Methods 48 (5):1043–59. doi:10.1080/03610926.2018.1429626.
   Web of Science ®Google Scholar
• Sarabia, J. M., and E. Gómez-Déniz. 2008. Construction of multivariate distributions: A review of some recent results (with discussion). Sort 32:3–36.
   Web of Science ®Google Scholar
• Sarabia, J. M., F. Prieto, and V. Jordá. 2014. Bivariate beta-generated distributions with applications to well-being data. Journal of Statistical Distributions and Applications 1 (15):1–35.
   Google Scholar
• Sklar, A. 1959. Fonctions de répartition à n dimensions et leurs marges. Publications de l'Institut de statistique de l'Université de Paris 8:229–31.
   Google Scholar
• Tahir, M. H., and G. M. Cordeiro. 2016. Compounding of distributions: A survey and new generalized classes. Journal of Statistical Distributions and Applications 3 (16):1–35.
   Google Scholar
• Visagie, I. J. H. 2018. On parameter estimation in multi-parameter distributions. Statistics, Optimization & Information Computing 6 (3):452–67. doi:10.19139/soic.v6i3.583.
   Google Scholar
• Zografos, K., and N. Balakrishnan. 2009. On families of beta and generalised gamma-generated distributions and associated inference. Statistical Methodology 6 (4):344–62. doi:10.1016/j.stamet.2008.12.003.
   Google Scholar