# 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 $$\Sigma = \begin{bmatrix} I_p & \rho J_p \\ \rho J_p & (1 + 0.5\kappa) I_p \end{bmatrix}$$. Then,

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