Comparisons of concordance in additive models

In this note we compare bivariate additive models with respect to their Pearson correlation coefficients, Kendall's τ concordance coefficients, and Blomqvist β medial correlation coefficients. The conditions that enable the comparisons involve variability stochastic orders such as the dispersive and the peakedness orders. Specifically we show that we can compare the Kendall's τ concordance coefficients of Cheriyan and Ramabhadran's bivariate gamma distributions, in spite of the fact that it is hard (and not necessary) to compute them.