# fourth_root¶

hyppo.tools.fourth_root(n, p, noise=False, low=- 1, high=1)

Fourth Root simulation.

Fourth Root $$(X, Y) \in \mathbb{R}^p \times \mathbb{R}$$:

$\begin{split}X &\sim \mathcal{U}(-1, 1)^p \\ Y &= |w^T X|^\frac{1}{4} + \frac{\kappa}{4} \epsilon\end{split}$
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.

• low (float, default: -1) -- The lower limit of the uniform distribution simulated from.

• high (float, default: 1) -- The upper limit of the uniform distribution simulated from.

Returns

x,y (ndarray of float) -- Simulated data matrices. x and `y have shapes (n, p) and (n, 1) where n is the number of samples and p is the number of dimensions.