erroneous moment values for t-distribution

[tcrensink]

<<Please describe the issue in detail here, and for bug reports fill in the fields below.>>

Moments of the t-distribution return incorrect values. See: https://en.wikipedia.org/wiki/Student%27s_t-distribution

• for df <= 1, the mean should be undefined
• for df < 1, the variance should be undefined

Example:

from scipy import stats
X = stats.t(df=0.8)
X.mean() # returns 0
X.var() # returns inf

Scipy/Numpy/Python version information:

1.0.0 1.14.0 sys.version_info(major=3, minor=6, micro=4, releaselevel='final', serial=0)

[josef-pkt]

AFAIK, the variance is inf and not undefined.
kurtosis is undefined because it divides by var (inf / inf)

[josef-pkt]

I take this back
because the mean is undefined for df <= 1, the var also has to be undefined