MNTEST <data>,<output_line> tests whether the active part of <data> is a random sample from a multivariate normal distribution. By default the multivariate measures of skewness and kurtosis presented by Mardia (1970) are computed and asymptotic test statistics related to them as well as their P values are presented. The test statistics are computed through principal components of the data. The actual dimension m of the distribution is determined by the sizes of eigenvalues. The proportion of the last accepted eigenvalue to the largest should exceed the value given by a specification EPS=<value> (default is EPS=1e-10). Since P values of Mardia's tests can be far from truth on small sample sizes, a sucro /MSKEW determines them by simulation. By specification TEST=MAHAL,<k> Mahanobis' distances of each observation from the mean are computed after determining the true dimesionality (say m) of data (by EPS). If data is a (large) sample from a multivariate normal distribution, these distances have an approximate chi^2 distribution with m degrees of freedom. This is tested by transforming the distances to uniform distribution on (0,1) by the distribution function of chi^2 and counting the # of observations in each of the <k> (default 10) subintervals. The uniformity of this frequency distribution is tested by the X^2 test and by the Kolmogorov-Smirnov test. By specification TEST=CUBE,<k> the data is mapped into a m-dimensional hypercube by computing principal components and transforming them into uniformly distributed values on (0,1). The dimension m is determined in the same way as in Mardia's tests. Thus in large multivariate normal samples the transformed data values are independently and uniformly distributed in the hypercube. For each observation, the maximum and minimum values (xmax and xmin) of m standardized (variance=1) principal component values are computed and and the observation is classified in two ways. In the first classification, it belongs to class # 1+int(k*F(xmax)^m) and in the second classification to class # 1+int(k*F(-xmin)^m) where F is the distribution function of the normal distribution. This means that in both classifications the frequencies should be distributed unformly in <k> classes (default is 10). Appropriate X^2 test is performed on this basis. Also the Kolmogorov-Smirnov test is made on the max and min values of the transformed data. 1 = More information on additional multivariate operations M = More information on multivariate analysis

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