Home → Troubleshooting → @RISK for Excel: Other Issues → 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