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Plot a histogram according to a set of rules using data from two tables
@Physicsworks I've addressed that (at least partially) in the edit to my answer. Depending on your data, you may not have the issue with observations that equal bin boundaries.
Confidence and prediction bands for custom nonlineal for CDF from ProbabilityDistribution
I don't think you're distribution is properly specified. Your CDF is not zero at x = 0. As a consequence, the PDF that Mma computes does not integrate to 1.