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Coefficient of Kurtosis Formula:
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The coefficient of kurtosis (β₂) is a statistical measure that describes the degree of peakedness or flatness of a probability distribution relative to the normal distribution. It quantifies the heaviness of the tails and the sharpness of the peak.
The calculator uses the coefficient of kurtosis formula:
Where:
Explanation: The coefficient compares the fourth moment of the distribution to the square of the variance, providing insight into the distribution's tail behavior and peak characteristics.
Details: Kurtosis helps identify whether a distribution has heavier or lighter tails than a normal distribution. High kurtosis indicates heavy tails and sharp peak (leptokurtic), while low kurtosis indicates light tails and flat peak (platykurtic).
Tips: Enter the fourth moment (μ₄) and standard deviation (σ) in consistent units. Both values must be positive. The result is dimensionless and indicates the distribution's kurtosis relative to normal distribution (β₂ = 3).
Q1: What does kurtosis measure?
A: Kurtosis measures the "tailedness" and peakedness of a probability distribution relative to the normal distribution.
Q2: What are the types of kurtosis?
A: Mesokurtic (β₂ = 3, normal), leptokurtic (β₂ > 3, heavy tails), and platykurtic (β₂ < 3, light tails).
Q3: How is kurtosis different from skewness?
A: Skewness measures asymmetry, while kurtosis measures tail heaviness and peak sharpness.
Q4: When is high kurtosis important?
A: High kurtosis is important in risk management, finance, and quality control as it indicates higher probability of extreme values.
Q5: Can kurtosis be negative?
A: The coefficient of kurtosis (β₂) is always positive since it's a ratio of positive quantities, but excess kurtosis (β₂ - 3) can be negative.