A comparison of normality tests towards convoluted probability distributions

References

• Adefisoye, J., Golam Kibria, B., & George, F. (2016). Performances of several univariate tests of normality: An empirical study. Journal of Biometrics and Biostatistics, 7 (4) , 1–10 https://doi.org/10.4172/2155-6180.1000322.
   Google Scholar
• Ahmad, F., & Khan, R. A. (2015). A power comparison of various normality tests. Pakistan Journal of Statistics and Operation Research, 11(3), 331–345. https://doi.org/10.18187/pjsor.v11i3.845
   Web of Science ®Google Scholar
• Anderson, T. W., & Darling, D. A. (1954). A test of goodness of fit. Journal of the American Statistical Association, 49(268), 765–769. https://doi.org/10.1080/01621459.1954.10501232
   Web of Science ®Google Scholar
• Barrera, N. P., Galea, M., Torres, S., & Villalón, M. (2006). Class of skew-distributions: Theory and applications in biology. Statistics, 40(4), 365–375. https://doi.org/10.1080/02331880600741780
   Web of Science ®Google Scholar
• Bono, R., Blanca, M. J., Arnau, J., & Gómez-Benito, J. (2017). Non-normal distributions commonly used in health, education, and social sciences: A systematic review. Frontiers in Psychology, 8, 1–6. https://doi.org/10.3389/fpsyg.2017.01602
   Web of Science ®Google Scholar
• Brandt, S. (1970). Statistical and computational methods in data analysis. Neuropadiatrie, 2(2). https://doi.org/10.1055/s-0028-1091858;https://www.jstor.org/stable/2335012
   Google Scholar
• D’Agostino, R. B. (1971). An omnibus test of normality for moderate and large size samples. Biometrika, 58(2), 341–348. https://doi.org/10.1093/biomet/58.2.341
   Web of Science ®Google Scholar
• D’Agostino, R., & Pearson, E. S. (1973). Tests for departure from normality. Empirical results for the distributions of b2 and √b1. Biometrika, 60(3) , 613–622 https://doi.org/10.2307/2335012.
   Web of Science ®Google Scholar
• Dominguez, A. (2015). A history of the convolution operation [Retrospectroscope]. IEEE Pulse, 6(1), 38–49. https://doi.org/10.1109/MPUL.2014.2366903
   Web of Science ®Google Scholar
• Gel, Y. R., & Gastwirth, J. L. (2008). A robust modification of the Jarque–Bera test of normality. Economics Letters, 99(1), 30–32. https://doi.org/10.1016/j.econlet.2007.05.022
   Web of Science ®Google Scholar
• Grinstead, C. M., & Snell, J. L. (2012). Introduction to probability. American Mathematical Soc.
   Google Scholar
• Hain, J. (2010). Comparison of common tests for normality. Diploma Thesis, Julius-Maximilians-Universität of Würzburg.
   Google Scholar
• Jarque, C. M., & Bera, A. K. (1987). A test for normality of observations and regression residuals. International Statistical Review/Revue Internationale de Statistique 55(2) , 163–172 https://doi.org/10.2307/1403192.
   Web of Science ®Google Scholar
• Kang, J. S., Kim, S. L., Kim, Y. H., & Jang, Y. S. (2010). Generalized convolution of uniform distributions. Journal of Applied Mathematics & Informatics, 28(5–6) , 1573–1581 https://koreascience.kr/article/JAKO201008758942063.pdf.
   Google Scholar
• King, G., Tomz, M., & Wittenberg, J. (2000). Making the most of statistical analyses: Improving interpretation and presentation. American Journal of Political Science, 44(2), 347–361. https://doi.org/10.2307/2669316
   Web of Science ®Google Scholar
• Lilliefors, H. W. (1967). On the Kolmogorov-Smirnov test for normality with mean and variance unknown. Journal of the American Statistical Association, 62(318), 399–402. https://doi.org/10.1080/01621459.1967.10482916
   Web of Science ®Google Scholar
• Lumley, T., Diehr, P., Emerson, S., & Chen, L. (2002). The importance of the normality assumption in large public health data sets. Annual Review of Public Health, 23(1), 151–169. https://doi.org/10.1146/annurev.publhealth.23.100901.140546
   PubMed Web of Science ®Google Scholar
• Maas, C. J., & Hox, J. J. (2004). The influence of violations of assumptions on multilevel parameter estimates and their standard errors. Computational Statistics & Data Analysis, 46(3), 427–440. https://doi.org/10.1016/j.csda.2003.08.006
   Web of Science ®Google Scholar
• Mbah, A. K., & Paothong, A. (2015). Shapiro–Francia test compared to other normality test using expected p -value. Journal of Statistical Computation and Simulation, 85(15), 3002–3016. https://doi.org/10.1080/00949655.2014.947986
   Web of Science ®Google Scholar
• Monhor, D. (2005). On the relevance of convolution of uniform distributions to the theory of errors. Acta Geodaetica et Geophysica Hungarica, 40(1), 59–68. https://doi.org/10.1556/AGeod.40.2005.1.5
   Google Scholar
• Noughabi, H. A., & Arghami, N. R. (2011). Monte Carlo comparison of seven normality tests. Journal of Statistical Computation and Simulation, 81(8), 965–972. https://doi.org/10.1080/00949650903580047
   Web of Science ®Google Scholar
• Pogány, T. K., & Nadarajah, S. (2013). On the convolution of normal and t random variables. Statistics, 47(6), 1363–1369. https://doi.org/10.1080/02331888.2012.694447
   Web of Science ®Google Scholar
• R Core Team (2020). R: A language and environment for statistical computing. R Foundation for Statistical Computing. https://www.R-project.org/
   Google Scholar
• Sackrowitz, H., & Samuel-Cahn, E. (1999). P values as random variables—expected P values. The American Statistician, 53(4) , 326–331 https://doi.org/10.2307/2686051.
   Web of Science ®Google Scholar
• Shapiro, S. S., & Wilk, M. B. (1965). An analysis of variance test for normality (complete samples). Biometrika, 52(3–4), 591–611. https://doi.org/10.1093/biomet/52.3–4.591
   Web of Science ®Google Scholar
• Shapiro, S. S., & Francia, R. (1972). An approximate analysis of variance test for normality. Journal of the American Statistical Association, 67(337), 215–216. https://doi.org/10.1080/01621459.1972.10481232
   Web of Science ®Google Scholar
• Sitek, G. (2020). Sum of gamma and normal distribution. Zeszyty Naukowe. Organizacja i Zarządzanie/Politechnika Śląska, (143), 275–284 https://doi.org/10.29119/1641-3466.2020.143.22 .
   Google Scholar
• Thadewald, T., & Büning, H. (2007). Jarque–Bera test and its competitors for testing normality–a power comparison. Journal of Applied Statistics, 34(1), 87–105. https://doi.org/10.1080/02664760600994539
   Web of Science ®Google Scholar
• Wijekularathna, D. K., Manage, A. B. W., & Scariano, S. M. (2022). Power analysis of several normality tests: A Monte Carlo simulation study. Communications in Statistics - Simulation and Computation, 51(3), 757–773. https://doi.org/10.1080/03610918.2019.1658780
   Google Scholar
• Yap, B. W., & Sim, C. H. (2011). Comparisons of various types of normality tests. Journal of Statistical Computation and Simulation, 81(12), 2141–2155. https://doi.org/10.1080/00949655.2010.520163
   Web of Science ®Google Scholar
• Yazici, B., & Yolacan, S. (2007). A comparison of various tests of normality. Journal of Statistical Computation and Simulation, 77(2), 175–183. https://doi.org/10.1080/10629360600678310
   Web of Science ®Google Scholar
• Zamanzade, E., & Arghami, N. R. (2011). Goodness-of-fit test based on correcting moments of modified entropy estimator. Journal of Statistical Computation and Simulation, 81(12), 2077–2093. https://doi.org/10.1080/00949655.2010.517533
   Web of Science ®Google Scholar
• Zamanzade, E., & Arghami, N. R. (2012). Testing normality based on new entropy estimators. Journal of Statistical Computation and Simulation, 82(11), 1701–1713. https://doi.org/10.1080/00949655.2011.592984
   Web of Science ®Google Scholar
• Zamanzade, E., & Mahdizadeh, M. (2017). Entropy estimation from ranked set samples with application to test of fit. Revista Colombiana de Estadística, 40(2), 223–241. https://doi.org/10.15446/rce.v40n2.58944
   Google Scholar