I'm developing a tool to conduct expert elicitations of scientists. As answers to questions are speculative, we like experts to help us understand the range of answers they find plausible, to get some idea of uncertainty.
For one type of question, we have them input a lower-bound, upper-bound, 25th percentile, 50th percentile and median (essentially the "5 number summary").
In testing we found that some scientists find this data intuitive, and others find it easier to visualize in the form of a PDF. I'm trying to figure out a straightforward algorithm to provide a PDF-style visualization of this "5 number summary". I've considered a "Skew Normal" distribution, would this be a good choice?
Put another way: given a quartiles+median, what's the most straightforward function to render a PDF for a distribution with those characteristics?
Any suggestions? I know this is sloppy at best, but the answers to these questions are speculative themselves, and we'll get better answers if we can communicate both ways.