This is a new addition to my diagnostic tool kit. I had never used Box Percentile plot before. However this week, I had to look at outliers in a data. Histograms are not that good for outliers. Box Plots, same story(though whiskers in the box plot are useful in getting an idea about the data points 1.5 IQR away from the boxes). I usually prefer Box plots for the simple reason that it gives a sense of the data from a quartiles perspective. . However most of the times you are interested in knowing more about them from a diagnostic perspective.

Box-Percentile plots build on the widely popular box plots and add a twist. One of the dimensions of the box in the box plot is not used. Look at the following figure of samples from Normal, Uniform w/outliers, Trimodal. All the box plots show the same illustration.
Box Percentile plots tries to use one of the box to the convey the same data, this giving a sense of outliers. They combine percentile plots which show ALL the data and box plot which is focused more on IQR.

Image

Now whatever is written above is angrezi…Here’s the math behind it.
If x_1,x_2…..x_n are ordered data points , then the data point x_k is plotted at a height wk/(n+1) if x_k is less than median, else it is plotted at a height (n+1-k)w/(n+1), where w is the desired width of the box….width is proportional to the percentile of the height

So, by construction , box-percentile plots give more information about the univariate distributions.