Sentence examples for bivariate case from inspiring English sources

aFor simplicity we consider the bivariate case.

A bivariate case of the proposed multivariate model is presented.

For the bivariate case it is adapted as follows.

Hence, we will propose the bivariate case in the following.

In what follows, we introduce the Lipschitz class in the bivariate case.

In [18], the approximation properties given by Gal in the complex plane was extended to the bivariate case.

In what follows, we will focus on the application of MECC for bivariate cases through examples.

Then, we applied these parallel numerical integration algorithms in the DuQMoGeM solution of the PBE for three bivariate cases, obtaining speedups between 11 and 15.

Performance for the bivariate cases where and is illustrated in Figure 3 and for the cases where and in Web Figures 6 8.

But to provide at least some perspective, simulations were run again for the bivariate normal case where σ 1=1 and σ 2=1.5.

However, in time series data, and, in particular, in conditional heteroscedastic time series, none of these assumptions hold and hence the behaviour of these measures is not that good as postulated for the bivariate Gaussian case.