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Original Articles

A truncated Cramér–von Mises test of normality

Pages 3956-3975 | Received 09 Mar 2017, Accepted 06 Apr 2018, Published online: 06 Jun 2019

References

  • Anderson, T. W., and D. A. Darling. 1954. A test of goodness of fit. Journal of American Statistics Association 49:765–69. doi: 10.2307/2281537.
  • de Wet, T., and J. Venter. 1973. Asymptotic distributions for quadratic forms with applications to test of fit. The Annals of Statistics 2:380–87. doi: 10.1214/aos/1176342378.
  • del Barrio, E., J. A. Cuesta Albertos, C. Matrán, and J. Rodríguez Rodríguez. 1999. Tests of fit based on the L2-Wasserstein distance. Annals of Statistics 27:1230–39. doi: 10.1214/aos/1017938923.
  • Cramér, H. 1928. On the composition of elementary errors. Second paper: Statistical applications. Skand. Aktuartidskr. 11:141–80. doi: 10.1080/03461238.1928.10416872.
  • Csörgó, S., and J. Faraway. 1996. The exact and asymptotic distributions of Cramér–von Mises statistics Journal of the Royal Statistics Society B 58 (1):221–34. doi: 10.1111/j.2517-6161.1996.tb02077.x.
  • Durbin, J. 1973. Weak convegence of the sample distribution when parameters are estimated. Annals of Statistics 1:219.
  • Fisher, R. A. 1930. The moments of the distribution for normal samples of measures of departure from normality. Proceedings of Royal Society, A 130:16. doi: 10.1098/rspa.1930.0185.
  • Gan, F. F., and K. J. Koelher. 1990. Goodness of fit tests based on P–P probability plots. Technometrics 32:289–303. doi: 10.2307/1269106.
  • Kalemkerian, J. 2017. An integral formula for the distribution of self-normalized Gaussian random samples. Communications in Statistics. Theory and Methods 46 (10):4671–85. doi: 10.1080/03610926.2015.1060335.
  • Lockhart, R. A., and M. A. Stephens. 1998. The probability plot: Test of fit based on the correlation coefficient. In Order statistics: Applications. Handbook of statistics, Vol. 17, 453–73. Amsterdam: North Holland.
  • Pearson, K. 1895. Contributions to the mathematical theory of evolution. Philosophical Transactions of the Royal Society 91:343. doi: 10.1098/rsta.1895.0010.
  • Pearson, E. S. 1930. A further development of tests for normality. Biometrika 22:239–49. doi: 10.2307/2332073.
  • Pettitt, A. N. 1976. Cramér–von Mises statistics for testing normality with censored samples. Biometrika 63 (3):475–81. doi: 10.2307/2335724.
  • Pettitt, A. N., and M. A. Stephens. 1976. Modified Cramér–von Mises statistics with censored samples. Biometrika 63 (2):291–98. doi: 10.2307/2335622.
  • Shapiro, S. S., and M. B. Wilk. 1965. An analysis of variance test for normality (complete samples). Biometrika 64: 415–18.
  • Shorack, G., and J. Wellner. 1982. Limit theorems and inequalities for the uniform empirical processes indexed by intervals. The Annals of Probability 10 (3):639–52. doi: 10.1214/aop/1176993773.
  • Skorokhod, A. 1956. Limit theorem for stochastic processes. Theory of Probability and its Applications 1:261–90. doi: 10.1137/1101022.
  • Smirnov, N. V. 1936. Sur la distribution de w2 (Critérium de M. R. von Mises). Comptes Rendus de l’Académie des Sciences 202:449–52.
  • Smirnov, N. V. 1937. Sur la distribution de w2 (Critérium de M. R. von Mises). Matematicheskij Sbornik (in Russian with French summary) 2:973–93.
  • Stephens, M. A. 1974. EDF Statistics for goodness of fit and some comparisons. JASA 79:730–37. doi: 10.2307/2286009.
  • Stephens, M. A. 1986. Tests based on EDF statistics. In Goodness of fit techniques. R. B. D’Agostino and M. A. Stephens, eds., Amsterdam: North-Holland.
  • Thadewald, T., and H. Buning. 2007. Jarque-Bera test and its competitors for testing normality—a power comparison. Journal of Applied Statistics 34:87–105. doi: 10.1080/02664760600994539.
  • von Mises, R. 1931. Wahrscheinlichkeitsrechnung. Vol. 21, Deuticke, Vienna.
  • Williams, P. 1935. Note on the sampling distribution of β2 , where the population is normal. Biometrika 27:269–71. doi: 10.2307/2332048.

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