A way to overcome this issue is to construct counterfactual distributions that integrate the conditional distribution of Y in a certain group given X over the distribution of X in the other group. Different approaches exist to estimate such counterfactual distributions but the simplest is to replace the distribution of population characteristics of a certain group by the distribution of X in the other group. This requires computing a reweighting factor w'hich can be estimated using a simple logit or probit model for the probability of belonging to this latter group. The inverting function is then defined as Recentered influence Function (RIF) for which the law of Iterated Expectations holds so that a full Oaxaca-Blinder decomposition of the RIF for the quantile of interest can be performed.