Many measurements of astronomical objects involve transverse vectors, directions tangent to the Celestial Sphere, such as polarization vectors, jets, major and minor axes, to name a few. Applying the Hub Test to a sample of transverse vectors yields measures of the correlations among the vectors' directions. How well do the directions aim toward points on the sphere, i.e. do they convergence? Do the directions avoid some point on the sphere, i.e. do they divergence? Judging significance requires developing statistics of samples of randomly directed transverse vectors, which is what this paper describes. Many artificial samples with randomly directed transverse vectors are created and the Hub Test is applied to each. The many results make distributions that are fit by suitable formulas. Thus probability distributions can be recovered by knowledge of the parameters, a great reduction in storage space. The collection of parameters for the many distributions makes the reference Library, a compact archive of statistical information. Having such a Library streamlines the process of finding the significance of Hub Test results. Two computer programs are provided in the Appendices so that creating the distribution parameter data can be repeated.