I have been given quantiles (min, 25%, med, 75%, max) for items of data, along with the size of the data n. From these pieces of information I would like to obtain a random sample of data points.
Apart from the trivial solutions where n ≤ 5, is there any way of doing this?
My attempt at a solution:
After some research I believe my best option is to obtain a distribution from these quantiles and then use inverse transform sampling to randomly sample n items from a given distribution which would give me n random data points that roughly agreed with the quantiles given.
However I am struggling to find digestible reading material on how I can obtain this distribution, from domain knowledge I suspect this distribution will be highly negatively skewed (Gumbel minimum / minimum extreme distribution)
Here are some related threads:
Estimating a distribution based on three percentiles
Estimate distribution from 4 quantiles
https://www.johndcook.com/blog/2010/01/31/parameters-from-percentiles/