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)
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