Most recipes on statistical data processing in Mathematica, such as building histograms, deriving smoothed PDF and CDF distributions, etc., work with given raw data sets. For example, series of measurements. However, there can be situations, when input is an already processed histogram with given counts for given bins.
Would it be a good idea to reconstruct a fake raw distribution according to some simplified algorithms? For example, a list of all data falling into a bin located at its centre or all data uniformly distributed across the bin interval.
I would like to have such lists in order to do further processing and to have at hand the whole distribution analysis toolkit. Is there some function to achieve this straightforwardly? Or can such cumulated data can be handled with available statistical methods for raw data? Can something be done with
Update. Here is some example data supplied to us with no trace of origin.
bins: 60-100;100-200;200-300;300-500;500-1000;1000-2000;2000-3000; >3000 counts: 275; 320; 112; 65; 53; 44; 16; 15
Interesting particulars are: 1) this is a censored data (rightmost interval is open; and 2) there is a suspicion on the heavy-tailed distribution. Moments of such a distribution function would diverge, and its asymptotics would be
x^-n. For both cases statisticians have special caveats in handling. Are such caveats, specially for 1), treatable by Mathematica as well?