Closed form solution of correlation in doubly truncated or censored sample of bivariate log-normal distribution

In this study we present a closed form solution to the moments and, in particular, correlation of two log-normally distributed random variables, where the underlying log-normal distribution is potentially truncated and censored at both tails. Throughout the analysis we further assume that the parameters of the unconstrained bivariate log-normal distribution are known. The closed form solution also covers the cases where one tail is truncated and the other is censored.