uncorrelated_bernoulli¶
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hyppo.tools.uncorrelated_bernoulli(n, p, noise=False, prob=0.5)¶ Uncorrelated Bernoulli simulation.
Uncorrelated Bernoulli \((X, Y) \in \mathbb{R}^p \times \mathbb{R}\): \(U \sim \mathcal{B}(0.5)\), \(\epsilon_1 \sim \mathcal{N}(0, I_p)\), \(\epsilon_2 \sim \mathcal{N}(0, 1)\),
\[\begin{split}X &= \mathcal{B}(0.5)^p + 0.5 \epsilon_1 \\ Y &= (2U - 1) w^T X + 0.5 \epsilon_2\end{split}\]- 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.prob (
float, default:0.5) -- The probability of the bernoulli distribution simulated from.
- Returns
x,y (
ndarray) -- Simulated data matrices.x` and ``yhave shapes(n, p)and(n, 1)where n is the number of samples and p is the number of dimensions.