joint_normal

hyppo.tools.joint_normal(n, p, noise=False)

Joint Normal simulation.

Joint Normal $(X,Y)\in {\mathbb{R}}^p\times {\mathbb{R}}^p$: Let $\rho =\frac{1}{2}p$, $I_p$ be the identity matrix of size $p\times p$, $J_p$ be the matrix of ones of size $p\times p$ and $\mathrm{\Sigma }=\left[\begin{array}{cc}{I}_p& \rho J_p\\ \rho J_p& (1+0.5\kappa )I_p\end{array}\right]$. Then,

$$(X,Y)\sim \mathcal{N}(0,\mathrm{\Sigma })$$

Parameters

• n (int) -- The number of samples desired by the simulation (>= 5).

• p (int) -- The number of dimensions desired by the simulation (>= 1).

• noise (bool, default: False) -- Whether or not to include noise in the simulation.

Returns

x,y (ndarray of float) -- Simulated data matrices. x` and ``y have shapes (n, p) and (n, p) where n is the number of samples and p is the number of dimensions.

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