It can be expressed as follows. One important limitation of the OB decomposition is that it applies only to differences in the mean. While there have been different methods developed for decomposing general distributional statistics over the last 15 years, Firpo et al. ( Their idea is to use the Recentered Influence Function (RIF) for the distributional statistic of interest instead of the usual outcome variable as the dependent variable in a regression. Consider RIF (y , v) is the influence function corresponding to an observed income y for the distributional statistic of interest, v(Fy).