I have a summary of statistics and several percentiles generated from a set of data. This includes: average, standard, min, p10, p25, p50, p75, p90, p95, max

Is there a way to reconstruct the distribution of data from the previous numbers?

I tried to generate subsets of the distribution that satisfied the percentiles (

https://stackoverflow.com/questions/14547364/generate-distribution-given-percentile-ranks)

That worked quite well for examples like:

average, std, min, p10, p25, p50, p75, p90, p95, max

63.6118, 36.1138, 0, 0, 45.8822, 75, 100, 100, 100, 100

and very bad for examples such as:

average, 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 works well without having assumptions about the asymmetry of the underlying distribution or its modality (for example, unimodal versus multimodal)?

Any help is really appreciated!