A method for Sampling Bernoulli Variables

TL;DR

This paper presents a novel method for generating correlated or uncorrelated Bernoulli variables using the binary expansion of continuous random variables, enabling controlled correlation structures.

Contribution

It introduces a new approach leveraging binary expansion of continuous variables to generate Bernoulli variables with customizable correlation properties.

Findings

Binary expansion of symmetric densities yields equiprobable bits.

Uniform distribution produces independent Bernoulli variables.

Parameterized densities allow control over correlation between Bernoulli samples.

Abstract

We introduce new method for generating correlated or uncorrelated Bernoulli random variables by using the binary expansion of a continuous random variable with support on the unit interval. We show that when this variable has a symmetric probability density function around 12 , its binary expansion provides equiprobable bits over {0, 1}. In addition we prove that when the random variable is uniformly distributed over [0, 1], its binary expansion generates independent Bernoulli random variables. Moreover, we give examples where, by choosing some parameterized nonuniform probability density functions over [0, 1], samples of Bernoulli variables with specific correlation values are generated.