Why not fit the data more exactly with a non-parametric approach?
Non-parametric statistical methods (e.g., Kernel estimators) assume no knowledge and in return supply no insights. Non-parametric estimates are in effect black boxes, which are an unsatisfactory second resort. We can do—and do—much better than that. A parameterization of the distribution, if adequate information exists to peg down a model, can: a) incorporate all the known facts about the data and the underlying dynamics; b) provide a benchmark against which data can be assessed for errors or manipulation; and c) comprise meaningful parameters that in themselves reflect facts about the data or dynamics.
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