On Sep 2, 2:37 pm, Mark Dickinson <dicki...@gmail.com> wrote: > On Sep 2, 6:15 pm, Thomas Philips <tkp...@gmail.com> wrote: > > > I mis-spoke - the variance is infinite when df=2 (the variance is df/ > > (df-2), > > Yes: the variance is infinite both for df=2 and df=1, and Student's t > with df=1 doesn't even have an expectation. I don't see why this > would stop you from generating meaningful samples, though. > > > and you get the Cauchy when df=2. > > Are you sure about this? All my statistics books are currently hiding > in my mother-in-law's attic, several hundred miles away, but wikipedia > and mathworld seem to say that df=1 gives you the Cauchy distribution. > > > I made the mistake because the denominator is equivalent to the > > square root of the sample variance of df normal observations, > > As I'm reading it, the denominator is the square root of the sample > variance of *df+1* independent standard normal observations. I agree > that the wikipedia description is a bit confusing. > > It seems that there are uses for Student's t distribution with > non-integral degrees of freedom. The Boost library, and the R > programming language both allow non-integral degrees of freedom. > So (as Robert Kern already suggested), you could drop the test > for integrality of df. In fact, you could just drop the tests > on df entirely: df <= 0.0 will be picked up in the gammavariate > call. > > -- > Mark
To tell you the truth, I have never used it with a non-integer number of degrees of freedom, but that's not the same as saying that df should be an integer. When df is an integer, one can interpret the t- distribution as the ratio of a unit normal (i.e. N(0,1)) to the sample standard deviation of a set of df+1 unit normals divided by sqrt(df +1). However, as Robert Kern correctly observes, the distribution is defined for all positive non-integer df, though we then lose the above interpretation, and must think of it in abstract terms. The distribution has infinite variance when df=2 and an undefined mean when df<=1, but the code can still be used to generate samples. Whether or not these samples make sense is altogether another question, but it's easy enough to remmove the restrictions. -- http://mail.python.org/mailman/listinfo/python-list
