I have fitted (through maximum likelihood estimation of parameters) a number of leptokurtic probability density functions (i.e.
- student's t (with parameters $\nu, \mu$)
to two datasets that are measured at different times and have different sample sizes.
All are 2-parameter PDFs. The Student's t distribution is the best fit PDF in terms of the highest log-likelihood values for both datasets. The second best-fitting PDF has the AIC difference of more than 6.
- Intuitively speaking, what are the unique properties of the student's t distribution that differentiate it from the other leptokurtic PDFs (at least from the one listed here.)
- How should I interpret/explain that why the student's t distribution is the best-fitting PDF and the others are not?