Fitting an arbitrary distribution to a given mean/mode/median Given some combination of mean/mode/median, how would I go about generating a distribution that can fit an arbitrary combination?
For cases where mean = mode = median, I would just use a normal distribution. How could I generate a distribution with, say, mean=3.0, mode=4.0, and median=5.0?
I've searched around and couldn't find an answer for this, which suggests maybe it's a silly question. Apologies if that's the case
Edit: I'm looking to create a visualization that plots a distribution that reacts as you change the mean/mode/median with sliders. Partially for teaching purposes and partially as a programming exercise, I just want to make something I can show students to demonstrate why it's important to have those numbers.
Are there distributions with parameters that are easy to set up some optimization algorithm for, to hit a target mean/median/mode?

For roughly normal distributions, the median is roughly the weighted average of the mean, the mean and the mode. So a roughly normal distribution with mean of $3$ and mode of $4$ would have median of roughly $10/3$, nowhere near $5$.
In other words, the example above is implausible. Without some explanation for why the median is so unusual, not even between the median and the mode, it's hard to find a reasonable distribution matching the parameters.
Reasonable values of mean, median and mode can often be fit exactly to either a triangular or split-normal distribution.
