Home
Back
Kurtosis Formula:
| From: | To: |
Kurtosis is a statistical measure that describes the degree to which a probability distribution is peaked or flat relative to a normal distribution. It measures the "tailedness" of the distribution and helps identify outliers in the data.
The calculator uses the kurtosis formula:
Where:
Explanation: The formula calculates the fourth standardized moment, which measures the heaviness of the distribution's tails compared to a normal distribution.
Details: Kurtosis is crucial for understanding the shape of data distributions, identifying potential outliers, assessing risk in financial modeling, and validating statistical assumptions in various fields including finance, engineering, and social sciences.
Tips: Enter the fourth moment (μ₄) and standard deviation (σ) in their respective units. Both values must be positive numbers greater than zero for accurate calculation.
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: How is kurtosis different from skewness?
A: Skewness measures asymmetry of the distribution, while kurtosis measures the tailedness and peakedness relative to a normal distribution.
Q3: When is high kurtosis problematic?
A: High kurtosis indicates more outliers, which can affect statistical tests that assume normality and impact risk assessment in financial models.
Q4: Can kurtosis be negative?
A: The formula kurtosis cannot be negative since both numerator and denominator are positive. However, excess kurtosis (kurtosis - 3) can be negative.
Q5: What are common applications of kurtosis?
A: Used in finance for risk management, quality control processes, signal processing, and any field requiring analysis of distribution shapes and outlier detection.