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.

cubic

step