# multimodal_independence¶

hyppo.tools.multimodal_independence(n, p, prob=0.5, sep1=3, sep2=2)

Multimodal Independence data.

Multimodal Independence $$(X, Y) \in \mathbb{R}^p \times \mathbb{R}^p$$: $$U \sim \mathcal{N}(0, I_p)$$, $$V \sim \mathcal{N}(0, I_p)$$, $$U^\prime \sim \mathcal{B}(0.5)^p$$, $$V^\prime \sim \mathcal{B}(0.5)^p$$,

$\begin{split}X &= \frac{U}{3} + 2 U^\prime - 1 \\ Y &= \frac{V}{3} + 2 V^\prime - 1\end{split}$
Parameters
• n (int) -- The number of samples desired by the simulation (>= 5).

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

• prob (float, default: 0.5) -- The probability of the bernoulli distribution simulated from.

• sep1, sep2 (float, default: 3, 2) -- The separation between clusters of normally distributed data.

Returns

x,y (ndarray) -- 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.