I have a summary statistics and various percentiles generated from a data set. This include: mean, std, min, p10, p25, p50, p75, p90, p95, max
Is there a way to reconstruct the data distribution from the numbers above?
I tried generating subsets of the distribution that would satisfy the percentiles ( https://stackoverflow.com/questions/14547364/generate-distribution-given-percentile-ranks)
That worked fairly well for examples like:
mean, std, min, p10, p25, p50, p75, p90, p95, max
63.6118, 36.1138, 0, 0, 45.8822, 75, 100, 100, 100, 100
and very poorly for examples like:
mean, std, min, p10, p25, p50, p75, p90, p95, max
0.0346, 0.8115, 0, 0, 0, 0, 0.0016, 0.0092, 0.0338, 29.4324
Is there a method that would work well without having assumptions about the skewness of the underlying distribution or its modality (e.g., unimodal vs multi-modal)?
The overall goal here is to try to generate a data sample from this unknown distribution that would match the given summary statistics.
Any help is highly appreciated!