PR changes the way P(X>=Y) is calculated.
Instead of using the joint density pdf[X](u) pdf[Y](v) and integrating over 2D plane, it integrates pdf[X](t) cdf[Y](t) over (-inf,+inf) using R's built-in integrate(). It should be faster and more accurate.
However, the behaviour of integrate() is not perfect: for very small P-values the default rel.tol results in P-values with high relative error (same order of magnitude, but the digits are incorrect); reducing rel.tol helps, but then the method reports roundoff error for non-significant cases.
PR changes the way P(X>=Y) is calculated. Instead of using the joint density
pdf[X](u) pdf[Y](v)and integrating over 2D plane, it integratespdf[X](t) cdf[Y](t)over (-inf,+inf) using R's built-inintegrate(). It should be faster and more accurate. However, the behaviour ofintegrate()is not perfect: for very small P-values the defaultrel.tolresults in P-values with high relative error (same order of magnitude, but the digits are incorrect); reducingrel.tolhelps, but then the method reportsroundoff errorfor non-significant cases.