Kurtosis Calculator: Measure Distribution Tailedness

About Kurtosis

Kurtosis is a statistical measure that describes the shape of a probability distribution by quantifying its tailedness. In simpler terms, it indicates how often extreme values occur in a distribution. There are three types of kurtosis:

• Mesokurtic: Kurtosis is around 3 (excess kurtosis around 0). This is typical of a normal distribution.
• Platykurtic: Kurtosis is less than 3 (excess kurtosis is negative). Distributions are flatter with thinner tails than a normal distribution.
• Leptokurtic: Kurtosis is greater than 3 (excess kurtosis is positive). Distributions are more peaked with fatter tails than a normal distribution, indicating more outliers.

This calculator helps you compute kurtosis for a given set of values and their probabilities, aiding in understanding the nature of your data distribution. Formula for Kurtosis (population): $$ Kurtosis = \frac{E[(X - \mu)^4]}{\sigma^4} $$ Where:

• \( X \) is the random variable.
• \( \mu \) is the mean of the distribution.
• \( \sigma \) is the standard deviation of the distribution.
• \( E[\cdot] \) is the expectation operator.

The excess kurtosis, often used, is Kurtosis - 3, which is zero for a normal distribution.