(2010), is a robust variant of ULS because both of them work with a polychoric correlations matrix, but, when using RULS, this kind of correlation is the basis for obtaining the Ac matrix thereafter, which is involved in a freely distributed weighing W matrix, since observed variables do not fulfil the

multivariate normal distribution assumption.

Lastly, to highlight the advantage of using a mixture of DPs over existing clustering approaches, we applied our approach, a revised version of our approach using a mixture of

multivariate normal distributions rather than DPs, and Kmeans to the normal and chi-squared simulation scenarios.

In this article, we propose a mixture of three-component

multivariate normal distributions to fit the expression levels of miRNAs to identify DV miRNAs between cases and controls.

Each time, we simulate the m traits from a

multivariate normal distribution with a compound symmetry correlation matrix with correlation [rho].

Note that because the

multivariate normal distribution [mathematical expression not reproducible] for the normal copula is parameterized in terms of a product moment correlation [[SIGMA].sub.Z] = [([r.sub.ij]).sup.n.sub.i,j=1], we need to calculate the corresponding Pearson product moment correlation [r.sub.ij] for each pair of correlations of the original random variables [X.sub.1],...,[X.sub.n].

[y.sub.[DELTA]], [y.sub.2[DELTA]], ..., [y.sub.k[DELTA]] [member of] [R.sup.d] is used to denote the d-dimension observation vector at each sampling epoch; thus [y.sub.k[DELTA]] given the state x obeys d-dimension

multivariate normal distribution with [N.sub.d]([[mu].sub.x], [[SIGMA].sub.x]), x = 0, 1, and the probability density function is given by

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).

Values of the type I error rates of the LRT for the independence between two groups of variables under

multivariate normal distribution in small sample sizes, n=25, (Figure 1A) increased significantly with the increase in the number of variables.

When the error term obeyed a

multivariate normal distribution, Baranchik [4] proved that the PSR estimator dominated uniformly the SR estimator under the quadratic loss, and Ohtani [13] also proved that the SRSV estimator dominated uniformly the SR estimator under a balanced loss function.

Among their topics are matrix algebra, the

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

In the world of elliptical distributions (e.g., the

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

and it has the nature of

multivariate normal distribution (MVN).