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I have read on this site an explanation of the t-distribution, and was interested to read a similar one of the F-distribution. The textbooks I have read generally do not cover this topic.

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  • $\begingroup$ Could you please clarify what would constitute an "explanation" of a PDF? Do you mean a mathematical derivation or perhaps are you looking for insight into its principal qualitative features? $\endgroup$
    – whuber
    Aug 13, 2014 at 14:20
  • $\begingroup$ Insight into its principal qualitative features. The link in the OP is to an answer by Glen_b that to some extent provides such insight. Maybe a better example would have been this related answer also by @Glen_b: stats.stackexchange.com/a/110365/9162. Again, however, it relates to the t-distribution and not the F-distribution. Though the question in that instance was more restrictive, the answer seems to cover all the principal qualitative features of the t-distribution. The question and answer were both quite popular. $\endgroup$ Aug 14, 2014 at 2:03

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The t-distribution and F-distribution are different because of the two degrees of freedom (dof) values that go into the latter, as opposed to one dof value for the former. The PDF quickly degenerates for high F values because of the low probability one would see such a large F value jointly across one of the dof (the one usually measuring the number of independent variables minus one). For the t distribution, one doesn't need to consider this second dof factor. Some lecture slides covering this are on: Statistical Ideas.

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