Goodness-of-fit graphical assessment for a broad family of unimodal distributions

References

• Ayebo, A., and T. J. Kozubowski. 2003. An asymmetric generalization of Gaussian and Laplace laws. Journal of Probability and Statistical Science 1:187–210.
   Google Scholar
• Azzalini, A. 1985. A class of distributions which include the normal. Scandinavian Journal of Statistics 12:171–8. http://www.jstor.org/stable/4615982.
   Web of Science ®Google Scholar
• Azzalini, A. 2013. The skew-normal and related families. Cambridge: Cambridge University Press. doi:10.1017/CBO9781139248891.
   Google Scholar
• Cao, R., and G. Lugosi. 2005. Goodness-of-fit tests based on the kernel density estimator. Scandinavian Journal of Statistics 32 (4):599–616. http://www.jstor.org/stable/4616900. doi:10.1111/j.1467-9469.2005.00471.x.
   Web of Science ®Google Scholar
• Conover, W. J. 1999. Practical nonparametric statistics. 3rd ed. New York, NY: J. Wiley & Sons.
   Google Scholar
• D’Agostino, R. B. and M. A. Stephens. 1986. Goodness-of-fit techniques. New York, NY: Marcel Dekker, Inc.
   Google Scholar
• Delicado, P. and M. N. Goria. 2008. A small sample comparison of maximum likelihood, moments and L-moments methods for the asymmetric exponential power distribution. Computational Statistics & Data Analysis 52 (3):1661–73.
   Google Scholar
• Fernández, C., J. Osiewalski, and M. F. J. Steel. 1995. Modeling and inference with υ-spherical distributions. Journal of the American Statistical Association 90 (432):1331–40. doi:10.1080/01621459.1995.10476637.
   Web of Science ®Google Scholar
• Harvard Dataverse. 2017. Galton height data. doi:10.7910/DVN/T0HSJ1.
   Google Scholar
• Henze, N., and M. D. Jiménez-Gamero. 2019. A new class of tests for multinormality with i.i.d. and garch data based on the empirical moment generating function. Test 28 (2):499–521. doi:10.1007/s11749-018-0589-z.
   Web of Science ®Google Scholar
• Henze, N., and S. Koch. 2020. On a test of normality based on the empirical moment generating function. Statistical Papers 61 (1):17–29. doi:10.1007/s00362-017-0923-7.
   Web of Science ®Google Scholar
• Jäntschi, L. 2019. A test detecting the outliers for continuous distributions based on the cumulative distribution function of the data being tested. Symmetry 11 (6):835. doi:10.3390/sym11060835.
   Google Scholar
• Jäntschi, L. 2020. Detecting extreme values with order statistics in samples from continuous distributions. Mathematics 8 (2):216. doi:10.3390/math8020216.
   Web of Science ®Google Scholar
• Jiménez-Gamero, M. D., V. Alba-Fernández, J. Muñoz-García, and Y. Chalco-Cano. 2009. Goodness-of-fit tests based on empirical characteristic functions. Computational Statistics & Data Analysis 53 (12):3957–71. doi:10.1016/j.csda.2009.06.001.
   Web of Science ®Google Scholar
• Ley, C. 2015. Flexible modelling in statistics: Past, present and future. Journal de la Société Française de Statistique 156:76–96.
   Google Scholar
• Gupta, R. C., and R. D. Gupta. 2004. Generalized skew normal model. Test 13 (2):501–24. doi:10.1007/BF02595784.
   Web of Science ®Google Scholar
• Gupta, R. C., and R. D. Gupta. 2008. Analyzing skewed data by power normal model. Test 17 (1):197–210. doi:10.1007/s11749-006-0030-x.
   Web of Science ®Google Scholar
• R Core Team. 2017. R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. https://www.R-project.org/.
   Google Scholar
• Sánchez-Espigares, J. A., P. Grima, and L. Marco-Almagro. 2018. Visualizing type II error in normality tests. The American Statistician 72 (2):158–62. doi:10.1080/00031305.2016.1278035.
   Web of Science ®Google Scholar
• Sánchez-Espigares, J. A., P. Grima, and L. Marco-Almagro. 2019. Graphical comparison of normality tests for unimodal distribution data. Journal of Statistical Computation and Simulation 89 (1):145–54. doi:10.1080/00949655.2018.1539085.
   Web of Science ®Google Scholar
• Sánchez-Espigares, J. A., P. Grima, and L. Marco-Almagro. 2021. Mosaic normality test. Communications in Statistics - Theory and Methods 50 (23):5561–73. doi:10.1080/03610926.2020.1734828.
   Web of Science ®Google Scholar
• Stigler, S. M. 1986. The history of statistics. The measurement of uncertainty before 1900. Cambridge, MA: Harvard University Press.
   Google Scholar
• Tovar-Falón, R., H. Bolfarine, and G. Martínez-Flórez. 2020. The asymmetric alpha-power skew-t distribution. Symmetry 12 (1):82. doi:10.3390/sym12010082.
   Google Scholar
• Yazici, B., and S. Yolacan. 2007. A comparison of various tests of normality. Journal of Statistical Computation and Simulation 77 (2):175–83. doi:10.1080/10629360600678310.
   Web of Science ®Google Scholar
• Zhu, D., and V. Zinde-Walsh. 2009. Properties and estimation of asymmetric exponential power distribution. Journal of Econometrics 148 (1):86–99. doi:10.1016/j.jeconom.2008.09.038.
   Web of Science ®Google Scholar