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A test for normality based on the empirical distribution function

  • Hamzeh Torabi [1] ; Narges H. Montazeri [1] ; Aurea Grané [2] Árbol académico
    1. [1] Yazd University

      Yazd University

      Irán

    2. [2] Universidad Carlos III de Madrid

      Universidad Carlos III de Madrid

      Madrid, España

  • Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 40, Nº. 1, 2016, págs. 55-88
  • Idioma: inglés
  • Enlaces
  • Resumen

    • In this paper, a goodness-of-fit test for normality based on t he comparison of the theoretical and empirical distributions is proposed. Critical values are o btained via Monte Carlo for several sample sizes and different significance levels. We study and compar e the power of forty selected normality tests for a wide collection of alternative distributions. T he new proposal is compared to some tradi- tional test statistics, such as Kolmogorov-Smirnov, Kuipe r, Cramer-von Mises, Anderson-Darling, Pearson Chi-square, Shapiro-Wilk, Shapiro-Francia, Jarq ue-Bera, SJ, Robust Jarque-Bera, and also to entropy-based test statistics. From the simulation study results it is concluded that the best performance against asymmetric alternatives with support on the whole real line and alternative distributions with support on the positive real line is achi eved by the new test. Other findings de- rived from the simulation study are that SJ and Robust Jarque -Bera tests are the most powerful ones for symmetric alternatives with support on the whole re al line, whereas entropy-based tests are preferable for alternatives with support on the unit int erval

  • Referencias bibliográficas
    • Alizadeh Noughabi, H. and Arghami, N.R. (2012). General treatment of goodness-of-fit tests based on KullbackLeibler information. Journal of...
    • Alizadeh Noughabi, H. and Arghami, N.R. (2010). A new estimator of entropy. Journal of the Iranian Statistical Society, 9, 53–64.
    • Alizadeh Noughabi, H. and Arghami, N.R. (2013). Goodness-of-fit tests based on correcting moments of entropy estimators. Communications in...
    • Alizadeh Noughabi, H. and Arghami, N.R. (2011). Monte carlo comparison of seven normality tests. Journal of Statistical Computation and Simulation,...
    • Anderson, T.W. (1954). A test of goodness of fit. Journal of the American Statistical Association, 49, 765– 769.
    • Anscombe, F.J. and Glynn, W.J. (1983). Distribution of kurtosis statistic b2 for normal statistics.Biometrika, 70, 227–234.
    • Armitage, P. and Berry, G. (1987). Statistical Methods in Medical Research. Blackwell Scientific Publications, Oxford.
    • Bonett, D.G. and Seier, E. (2002). A test of normality with high uniform power. Computational Statistics and Data Analysis, 40, 435–445.
    • Chen, L. and Shapiro, S.S. (1995). An alternative test for normality based on normalized spacings. Journal of Statistical Computation and...
    • Corea, J.C. (1995). A new estimator of entropy. Communications in Statistics-Theory and Methods, 24, 2439–2449.
    • Cramer, H. (1928). On the composition of elementary errors. Scandinavian Actuarial Journal, 11, 141–180.
    • Csörgo, M. and Révész, P. (1971). Strong Approximations in Probability and Statistics. Academic Press, New York.
    • D’Agostino, R.B. and Stephens, M. (1986). Goodness-of-fit Techniques. New York: Marcel Dekker, Inc.
    • D’Agostino, R.B. and Pearson, E.S. (1973). Tests for departure from normality. Empirical results for the distributions of b2 and sqrtb1. Biometrika,...
    • D’Agostino, R.B., Belanger, A. and D’Agostino R.B.Jr. (1990). A suggestion for using powerful and informative tests of normality. The American...
    • D’Agostino, R.B. (1970). Transformation to Normality of the Null Distribution of g1. Biometrika, 57, 679– 681.
    • D’Agostino, R.B. (1971). An omnibus test of normality for moderate and large size samples. Biometrika, 58, 341–348.
    • del Barrio, E., Cuesta-Albertos, J.A., Matrán, C. and Rodrı́guez-Rodrı́guez, J.M. (1999). Tests of goodness of fit based on the L2-wasserstein...
    • de Wet, T. and Venter, J.H. (1972). Asymptotic distributions of certain tests criteria of normality. South African Statistical Journal, 6,...
    • Dimitriev, Y.G. and Tarasenko, F.P. (1973). On the estimation functions of the probability density and its derivatives. Theory of Probability...
    • Doornik, J.A. and Hansen, H. (1994). An omnibus test for univariate and multivariate normality. Economics Working Papers, Nuffield College.
    • Ebrahimi, N., Pflughoeft, K. and Soofi, S.E. (1994). Two measures of sample entropy. Statistics and Probability Letters, 20, 225–234.
    • Epps, T.W. and Pulley, L.B. (1983). A test for normality based on the empirical characteristic function. Biometrika, 70, 723–726.
    • Esteban, M.D., Castellanos, M.E., Morales, D. and Vajda, I. (2001). Monte carlo comparison of four normality tests using different entropy...
    • Filliben, J.J. (1975). The probability plot correlation coefficient test for normality. Technometrics, 17, 111– 117.
    • Gan, F.F. and Koehler, K.J. (1990). Goodness of fit tests based on P-P probability plots. Technometrics, 32, 289–303.
    • Gel, Y.R., Miao, W. and Gastwirth, J.L. (2007). Robust directed tests of normality against heavy-tailed alternatives. Computational Statistics...
    • Gel, Y.R. and Gastwirth, J.L. (2008). A robust modification of the Jarque-Bera test of normality. Economics Letters, 99, 30–32.
    • Grané, A. and Fortiana, J. (2003). Goodness of fit tests based on maximum correlations and their orthogonal decompositions. Journal of the...
    • Grané, A. (2012). Exact goodness of fit tests for censored data. Annals of the Institute of Statistical Mathematics, 64, 1187–1203.
    • Grané, A. and Tchirina, A. (2013). Asymptotic properties of a goodness-of-fit test based on maximum correlations. Statistics, 47, 202–215.
    • Henry, C. T. (2002). Testing for Normality. Marcel Dekker, New York.
    • Janssen, A. (2000). Global power functions of godness-of-fit tests. Annals of Statististics, 28, 239–253.
    • Jarque, C.M. and Bera, A.K. (1980). Efficient tests for normality, homoscedasticity and serial independence of regression residuals. Economics...
    • Jarque, C.M. and Bera, A.K. (1987). A Test for Normality of Observations and Regression Residuals. International Statistical Review/Revue...
    • Kolmogorov, A.N. (1933). Sulla determinazione empirica di una legge di dislibuzione. Giornale dell’Istitu Italiano degli Attuari, 4, 83–91.
    • Krauczi, E. (2009). A study of the quantile correlation test for normality. TEST,18, 156–165.
    • Kuiper, N.H. (1962). Test concerning random points on a circle. Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen Series...
    • LaRiccia, V. (1986). Optimal goodness-of-fit tests for normality against skewness and kurtosis alternatives. Journal of Statistical Planning...
    • Lilliefors, H.W. (1967). On the Kolmogorov-Smirnov test for normality with mean and variance unknown. Journal of the American Statistical...
    • Louter, A.S. and Koerts, J. (1970). On the Kuiper test for normality with mean and variance unknown. Statistica Neerlandica, 24, 83–87.
    • Martinez, J.and Iglewicz, B. (1981). A test for departure from normality based on a biweight estimator of scale. Biometrika, 68, 331–333.
    • Mises, R. von (1931). Wahrscheinlichkeitsrechnung und ihre Anwendung in der Statistik und theoretischen Physik. Deuticke, Leipzig and Vienna.
    • Pardo, L. (2006). Statistical Inference based on Divergence Measures. New York: Taylor Francis Group.
    • Park, S. and Park, D. (2003). Correcting moments for goodness-of-fit tests based on two entropy estimates. Journal of Statistical Computation...
    • Pettitt, A.N. (1977). A Cramer-von Mises type goodness of fit statistic related to √ b1 and b2. Journal of the Royal Statistical Society....
    • Poitras, G. (2006). More on the correct use of omnibus tests for normality. Economics Letters, 90, 304–309.
    • Romao, X., Delgado, R. and Costa, A. (2010). An empirical power comparison of univariate goodness-offit tests for normality. Journal of Statistical...
    • Shao, J. (2003). Mathematical Statistics. New York: Springer, Verlag.
    • Shapiro, S.S., Wilk, M.B. and Chen, M.H.J. (1968). A comparative study of various tests for normality. Journal of the American Statistical...
    • Shapiro, S.S. and Wilk, M.B. (1965). An analysis of variance test for normality (complete samples). Biometrika, 52, 591–611.
    • Shapiro, S.S. and Francia, R.S. (1972). An approximate analysis of variance test for normality. Journal of the American Statistical Association,...
    • Shenton, L. and Bowman, K. (1977). A bivariate model for the distribution of b1 and b2. Journal of the American Statistical Association, 72,...
    • Van Es, B. (1992). Estimating functionals related to a density by class of statistics based on spacing. Scandinavian Journal of Statistics,...
    • Vasicek, O. (1976). A test for normality based on sample entropy. Journal of the Royal Statistical Society. Series B: Methodological, 38,...
    • Watson, G.S. (1961). Goodness-of-fit tests on a circle. Technometrics, 48, 109–114.
    • Yap, B.W. and Sim, C.H. (2011). Comparisons of various types of normality tests. Journal of Statistical Computation and Simulation, 81, 2141–2155.
    • Yazici, B. and Yolacan, S. (2007). A comparision of various tets of normality. Journal of Statistical Computation and Simulation, 77, 175–183.
    • Zamanzade, E. and Arghami, N.R. (2012). Testing normality based on new entropy estimators. Journal of Statistical Computation and Simulation,...
    • Zhang, J. and Wu, Y. (2005). Likelihood-ratio tests for normality. Computational Statistics and Data Analysis, 49, 709–721.
    • Zhao, J. and Xu, X. (2014). Goodness-of-fit tests for location scale families based on random distance. Journal of Statistical Computation...
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