void StudentStat(Int32 Nu, ref Double AMean, ref Double AVariance, ref Double ASkewness, ref Double AKurtosis)
Student's t distribution moments (mean, variance, skewness, kurtosis).
| # | Name | Description |
|---|---|---|
| 1 | AMean | Returns the mean, = 0 |
| 2 | defined only for Nu > 1 (NAN otherwise). | |
| 3 | AVariance | Returns the variance, = Nu/(Nu-2) for Nu >= 3 |
| 4 | +INF for Nu < 3. | |
| 5 | ASkewness | Returns the skewness, = 0 |
| 6 | defined only for Nu > 3 (NAN otherwise). | |
| 7 | AKurtosis | Returns the FULL (non-excess) kurtosis, = (3 Nu - 6)/(Nu - 4) |
| 8 | defined only for Nu > 4 (NAN otherwise). Note | this is the full kurtosis, not the excess kurtosis (subtract 3 to obtain the excess form 6/(Nu-4)). |
| 9 | Nu | Degrees of freedom, integer >= 1. |
Result: stored in self (calling object)
Remarks:
Returns the moments of the Student's t distribution with nu degrees of freedom. Each moment exists only for sufficiently large nu: mean needs nu > 1, variance is finite for nu >= 3 (and +inf for nu < 3), skewness needs nu > 3 and kurtosis needs nu > 4; a moment whose condition is not met is returned as NAN. Unlike the other distributions in this unit, AKurtosis is the FULL kurtosis, not the excess kurtosis.