The R-code for computing the cdf and the df of the ratio of two correlated Normal rv

The cumulative distribution and the density function of the ratio of two correlated Normal random variables has been proposed and studied by Aroian (1986) and Oksoy and Aroian (1986, 1994) and Kim (2006). For a complete review and further insights on this topic, the interested reader is referred to Galeone (2007). In Galeone and Pollastri (2012a, 2013) the quantiles of this random are used to build confidence intervals for the ratio of two means and for the incremental cost-effectiveness ratio. Pollastri and Tulli (2012) have studied the distribution of absolute ratio of two correlated Normal random variables and used it to define the confidence interval for non-negative ratio indicators. In order to ease the computation of the cumulative distribution function (cdf), the density function (df), and of the quantiles of these ratio random variables, in the present note the R-codes are presented and exemplified.