signed_bernoulli2(N​,p1,p2,r)

Generate and Sample Two Signed Bernoulli Variables with Given Correlation

The function first constructs two(2) signed {-1, +1} Bernoulli variables Y_1, Y_2 such that p(Y_1 = -1) = p1, p(Y_2 = -1) = p2, and E[Y_1Y_2] = r. Constraints: 0 < p1,p2 < 1, -1 < r < 1. Next, it draws N realizations of the two variables in Y(m,:), m = 1,2. The sample pdf and cross correlation converge as N -> infinity (obviously).
Example: generate N realizations of variables with mean 0, variance 1, and correlation 0.3: Y = signed_bernoulli2(N,0.5,0.5,0.3).