I have a requirement of comparing two histograms. It is a distribution of buckets of time frames and each bucket has finite no. of entries.

An example of the histogram:

buckets - [2, 4, 8, 16, 32, 64, 128, 512, 1024, 2048] (It represents the time values)
values - [30000, 2500, 40000, 78801, 156666, 304528, 588000, 163680, 2859, 1] (It represents the no. of entries in the bucket)

The entry can be understood as a time taken to run some particular function. ith entry took time between [buckets[i-1], buckets[i]).

I tried approximating skewness by using the formula = ((3 * (mean - median)) / stddev). Here for each bucket, mean was taken as midpoint of the bucket. But the calculated skewness using this approach doesn't looks reliable with the actual skewness values I calculated on the raw data. So, is there any specific approach which I can use to compare such distributions?



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