DENSITY PROBABILITY PLOTS

Probability plots are popular and effective tools for the graphical assessment of the goodness-of-fit of a given dataset to a hypothesised probability distribution, F say, with density f. The user can easily see any departures from F that there are, but the interpretation of such departures may not be immediately apparent. (It may take some time to work out their meaning, or else to resort to a set of rules for the interpretation of probability plots.) We investigate whether instant interpretability of these tools can be aided by a simple transformation which transfers visual assessment to the realms of familiar and immediate comparisons between densities. We seek to do so without smoothing, and see how far this allows us to go. The idea is very effective, and rather more so than quantile-quantile plots, for f's that have a single peak when the density g from which the data truly come is also unimodal. The idea is much less appealing, however, when f and g have different modalities from each other.