I am using the scipy.stats.t.fit function, and I am surprised by the results. If I fit on some bimodal data, say
df=0.39126249808550329 loc=1.0 scale=5.7172845190830792e-21
That is, the scale is effectively zero, and I will never be able to sample anything near 5, just the more frequent data point 1.
I guess you really can't fit on data that is too different from a t-distribution - but is scipy really giving the best t dist fit to the data? I would think that if I compute a sample mean and variance myself, i.e,
df = 5 loc = 2.33 scale = 1.88
That I'd have a better fit, although I haven't computed the likelihood of sampling
[1,1,1,5,5] from these two t distributinos.