I have a histogram, where I count the number of occurrences that a function takes particular values in the range 0.8 and 2.2.
I would like to get the cumulative distribution function for the set of values. Is it correct to just count the total number of occurrences until each particular value.
For example, the cdf at 0.9 will be the sum of all the occurrences from 0.8 to 0.9?
Is it correct?
Thank you
The sum normalised by the number of entries will give you an estimate of the cdf, yes. It will be as accurate as the histogram is an accurate representation of the pdf. If you want to evaluate the cdf anywhere except the bin endpoints, it makes sense to include a fraction of the counts, so that if you have break points b_i and b_j, then to evaluate the cdf at some point b_i < p < b_j you should add the fraction of counts (p - b_i) / (b_j-b_i) from the relevant cell. Essentially this assumes uniform density within the cells.
You can get an estimate of the cdf from the underlying values, too (based on your question I'm not quite sure what you have access to, whether its bin counts in the histogram or the actual values). Beware that doing so will give your CDF discontinuities (steps) at each data point, so think about whether you have enough, and what you're using the CDF for, to determine whether this is appropriate.
As a final note of warning, beware that evaluating the cdf outside of the range of observed values will give you an estimated probability of zero or one (zero for x<0.8, one for x>2.2). You should consider whether the function is truly bounded to that interval, and if not, employ some smoothing to ensure small amounts of probability mass outside the range of observed values.
