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.

    Lösungsbeispiel

    Compute the kurtosis of the values 2, 4, 4, 6.

    1. Mean = (2 + 4 + 4 + 6) / 4 = 4
    2. Deviations: -2, 0, 0, 2
    3. m2 = (4 + 0 + 0 + 4) / 4 = 2
    4. m4 = (16 + 0 + 0 + 16) / 4 = 8
    5. Kurtosis = 8 / 4 = 2
    6. Excess Kurtosis = 2 - 3 = -1 (platykurtic)