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Kurtosis Formula:
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Kurtosis is a statistical measure that describes the shape of a probability distribution, specifically the "tailedness" of the distribution relative to a normal distribution. It indicates whether data are heavy-tailed or light-tailed relative to a normal distribution.
The calculator uses the Kurtosis formula:
Where:
Explanation: Kurtosis measures the combined weight of a distribution's tails relative to the center of the distribution. A normal distribution has a kurtosis of 3.
Details: Kurtosis is important in statistics for understanding the shape of data distributions. It helps identify outliers and assess risk in financial modeling, quality control processes, and various scientific research fields.
Tips: Enter the fourth moment (μ₄) and standard deviation (σ) values. Both values must be positive numbers. The result is dimensionless and represents the kurtosis of the distribution.
Q1: What do different kurtosis values indicate?
A: Kurtosis = 3 indicates mesokurtic (normal distribution), >3 indicates leptokurtic (heavy tails), and <3 indicates platykurtic (light tails).
Q2: Why is kurtosis important in finance?
A: High kurtosis indicates higher risk of extreme outcomes, which is crucial for risk management and investment strategies.
Q3: What is excess kurtosis?
A: Excess kurtosis = kurtosis - 3. It measures kurtosis relative to a normal distribution, making interpretation easier.
Q4: Can kurtosis be negative?
A: The formula kurtosis = μ₄/σ⁴ cannot be negative since both numerator and denominator are squared terms. However, excess kurtosis can be negative.
Q5: What are the limitations of kurtosis?
A: Kurtosis doesn't distinguish between left and right tails, and can be sensitive to outliers. It should be used with other statistical measures.