HomeTroubleshooting@RISK for Excel: Other IssuesDistribution Fitting Won't fit Student's t to My Data

8.21. Distribution Fitting Won't fit Student's t to My Data

Applies to:
@RISK Professional and Industrial Editions, all releases

@RISK will fit other distributions to my data set, but for some reason it won't fit a Student's t, and in the fit results that distribution is grayed out. Why?

Distribution fitting is an iterative process: @RISK keeps tweaking the parameters of a candidate distribution until it has the parameters that do the best job for that distribution, then moves on to the next candidate distribution. Fitting to a Student's t is problematic for some data sets.

Suppose the data set is a good fit to a normal distribution. Well, as Student's t increases the number of degrees of freedom (df), the distribution gets closer and closer to a normal. If you could have such a thing as a Student's t with an infinite number of df, it would be a normal.

What will an iterative fitting process do with data that are really normal, when trying to fit a Student's t? It will try a particular number of df, then try df+1 and see that it's a better fit, try df+2 and see that it's still better, ... and the process could continue without end. No matter the df, a higher number would be a better fit. For such data sets, there is no best fit to a Student's t, because a better fit always exists at a higher df. (It's equivalent to trying to find the largest number less than 1.)

Therefore @RISK is unable to report a best fit of a Student's t distribution to your data. One or more of the distributions that it does fit will be a better fit for your data set than any possible Student's t.

Last edited: 2018-08-18

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