Kurtosis Calculator
Estimate kurtosis to measure whether data tails are heavier or lighter than a normal distribution.
Kurtosis
2.0000
Kurtosis vs Value 1
Formula
## 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.
Exemplo Resolvido
Compute the kurtosis of the values 2, 4, 4, 6.
- 01Mean = (2 + 4 + 4 + 6) / 4 = 4
- 02Deviations: -2, 0, 0, 2
- 03m2 = (4 + 0 + 0 + 4) / 4 = 2
- 04m4 = (16 + 0 + 0 + 16) / 4 = 8
- 05Kurtosis = 8 / 4 = 2
- 06Excess Kurtosis = 2 - 3 = -1 (platykurtic)
Perguntas Frequentes
What does high kurtosis indicate?
High excess kurtosis (positive) means the tails are heavier than a normal distribution, so extreme values are more likely. Financial returns often show high kurtosis.
What is the kurtosis of a normal distribution?
A normal distribution has a kurtosis of exactly 3, or equivalently an excess kurtosis of 0.
Is kurtosis about peakedness?
A common misconception equates kurtosis with peakedness, but kurtosis primarily measures the weight of the distribution tails, not the height of the peak.
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