Kurtosis Rechner — Formel
## How to Calculate Kurtosis
### Formula
**Kurtosis = m4 / m2^2**
where m4 is the fourth central moment and m2 is the second central moment (variance).
**Excess Kurtosis = Kurtosis - 3**
- Excess kurtosis > 0: Leptokurtic (heavier tails than normal)
- Excess kurtosis = 0: Mesokurtic (similar to normal)
- Excess kurtosis < 0: Platykurtic (lighter tails than normal)
The normal distribution has a kurtosis of 3, so subtracting 3 gives excess kurtosis relative to normal.
### Formula
**Kurtosis = m4 / m2^2**
where m4 is the fourth central moment and m2 is the second central moment (variance).
**Excess Kurtosis = Kurtosis - 3**
- Excess kurtosis > 0: Leptokurtic (heavier tails than normal)
- Excess kurtosis = 0: Mesokurtic (similar to normal)
- Excess kurtosis < 0: Platykurtic (lighter tails than normal)
The normal distribution has a kurtosis of 3, so subtracting 3 gives excess kurtosis relative to normal.
Lösungsbeispiel
Compute the kurtosis of the values 2, 4, 4, 6.
- Mean = (2 + 4 + 4 + 6) / 4 = 4
- Deviations: -2, 0, 0, 2
- m2 = (4 + 0 + 0 + 4) / 4 = 2
- m4 = (16 + 0 + 0 + 16) / 4 = 8
- Kurtosis = 8 / 4 = 2
- Excess Kurtosis = 2 - 3 = -1 (platykurtic)