Using the sum-of-uniforms method to generate correlated random variates with certain marginal distribution
This paper extends the sum-of-uniforms method to generate correlated random variables with certain marginal distributions. We first use the transformation method to derive the joint probability density function of the correlated uniform random variables. We also demonstrate that the sum-of-uniforms method can be extended to generate correlated random variables with certain marginal distributions including uniform, exponential, Erlang, Bernoulli, binomial, geometric, and negative binomial. Finally, this paper presents the exact correlation coefficients of such correlated random variables.
correlated random variates simulation multivariate generation