I have many customers. Each generates his own distribution of shopping times. Each customer thus has their own empirical distribution of shopping times.
If I want to get a sense of the average within-person variation (distribution, really) in trip times, how might I go about doing this? I don't want to just look at the aggregate distribution of trip times since that could be simply driven by between-person heterogeneity in shopping times. Ex. half the people shop at one time and half shop at another time would have no within-person variation, so the total distribution is wrong. Also the distribution of trip times might vary systematically with how often they shop, so this would overweight those people (when I don't want to in this case.)
Additionally, I don't want to use some summary statistic like variance for each customer and the plot the distribution of those. Is there something richer that can be done in these panel type situations?