Ellipse denotes quantile of 95% in

multivariate normal distribution (Santos-Fernandez 2012).

In order to test the validity of

multivariate normal distribution for the evaluated data, ordered squares of the mahalanobis distances calculated individually for each (experimental unit) animal were estimated by using PROC IML of SAS program as reported earlier by Eyduran and Akbas (2010).

Thus, the objective of this study was to calculate the type I error and the power of the LRT for determining the independence between two groups of castor oil plant traits under a

multivariate normal distribution in scenarios consisting of the combinations of 16 sample sizes; 40 combinations of the number of traits from the two groups; and nine degrees of correlation between the traits (for the power).

The Wishart distribution, which is the distribution of the sample variance covariance matrix when sampling from a

multivariate normal distribution, is a special case of the matrix variate gamma distribution.

from m-dimensional

multivariate normal distribution [b.

Thirdly, when the randomness of uncertain return rate vector follows

multivariate normal distribution, the covariance matrix can reflect the interactions and correlation degrees among securities.

But the

multivariate normal distribution has asymptotic independence, such that events, regardless of the strength of their correlation, become independent if one pushes far enough into the tails (Embrechts, McNeil, and Straumann 2002).

Thus, multivariate samples with outliers were generated in contaminated

multivariate normal distribution, and outlier percentage was specified in multivariate t-distribution by mixing probability [delta], proportions 0.

For the Gaussian copula, it is to be noted that with Gaussian marginals, it in effect results in a

multivariate normal distribution, that is, we have

Among their topics are matrix algebra, the

multivariate normal distribution, tests on covariance matrices, principle component analysis, cluster analysis, and graphical procedures.

the

multivariate normal distribution or multivariate t-distribution), it is an acceptable metric.

For

multivariate normal distribution, we organized the data into an n X p matrix, X, where the p columns were measurements and calculated values, and the n row vectors were the 3 attributes: [log.