Kurtosis Explorer: Moments Comparison with Advice
Degrees of Freedom (df):
10
1
30
Moment
Standard Normal
t-Distribution
Mean
0
0.000
Standard Deviation
1
1.118
Kurtosis (Excess)
0
1.000
Moderate degrees of freedom; t-distribution has heavier tails than normal, so tests are more conservative.
Alternative approaches:
For low degrees of freedom, consider robust or non-parametric tests, or Bayesian methods that model heavy tails.
−5
−4
−3
−2
−1
0
1
2
3
4
5
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Standard Normal
t-Distribution (df=10)
Normal vs t-Distribution (varying kurtosis)
x
Probability Density
plotly-logomark