Kurtosis is a statistical measure that describes the shape of a probability distribution’s tails in relation to its overall shape. Specifically, it assesses the presence of outliers by evaluating the extremity of data points in the distribution’s tails.
Understanding Kurtosis:
- Definition: Kurtosis quantifies the “tailedness” of a distribution, indicating how much of the distribution’s variance is due to infrequent extreme deviations, or outliers.
- Calculation: Mathematically, kurtosis is defined as the fourth central moment divided by the square of the variance. This formula measures the weight of the distribution’s tails relative to its center.
Types of Kurtosis:
- Mesokurtic: A distribution with kurtosis similar to that of a normal distribution, indicating a moderate level of outliers.
- Leptokurtic: A distribution with positive kurtosis, characterized by heavy tails and a sharp peak, suggesting a higher likelihood of outliers.
- Platykurtic: A distribution with negative kurtosis, featuring light tails and a flatter peak, indicating fewer outliers.