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Constructing an empirical distribution from data



You have a set of random and representative observations of a single model variable, for example the number of children in American families (we'll look at a joint distribution for two or more variables at the end of this section), and you have enough observations to feel that the range and approximate random pattern has been captured. You want to use the data to construct a distribution directly.


It is unnecessary to fit a distribution to the data: instead one can simply use the empirical distribution of the data (if there are no physical or biological reasons a certain distribution should be used, we generally prefer an empirical distribution). Below, we outline three options you have to use this data to construct an empirical distribution:


Model Empirical_distributions (sheet Histogram) provides an example.



Creating an empirical joint distribution for two or more variables

For data that are collected in sets (pairs, triplets, etc), there may be correlation patterns inherent in the observations, and that we would like to maintain while fitting empirical distributions to data. An example is data of people's weight and  height, where there is clearly  some relationship between them. A combination of using Crystal Ball's Discrete Uniform distribution with an Excel VLOOKUP() or OFFSET( ) function allows us to do this easily.