The distribution of the absolute value of the ratio of two correlated normal random variables

The aim of this paper is to study the distribution of the absolute quotient of two Correlated Normal random variables (r.v.s). This study may have many applications, as often the researcher expects a ratio to be positive or considers the sign of the ratio unimportant. Taking into account a form of the distribution of the ratio of two Correlated Normal r.v.s proposed by Oksoy and Aroian in 1986 and further studied in 1994, we find the distribution of the absolute quotient of two correlated Normal r.v.s. The form proposed here is simple to compute, as it is a function of the T (h; λ) studied by Owen in 1956. We also represent the distribution of the absolute ratio as a function of the distribution of the Arctangent r.v.. Some examples regarding the confidence intervals for indicators used to evaluate the relative errors of the invoices reveal the importance of the distribution of the absolute ratio of two Correlated Normal r.v.s, here presented.