Kurtosis is a statistical measure that describes the shape of a probability distribution's tails in relation to a normal distribution. It helps determine whether a dataset has extreme outliers or how "peaked" the distribution is.

Types of Kurtosis

1. Mesokurtic (Normal Kurtosis, ≈ 3)

   • The data follows a normal distribution.
   • Example: Standard normal distribution.
   • Interpretation: No extreme tails, moderate peak.

2. Leptokurtic (Kurtosis > 3, "Heavy-Tailed")

   • The distribution has fat tails (more extreme outliers).
   • Data is more concentrated in the center but has extreme values.
   • Example: Stock market crashes, financial risk models.
   • Interpretation: Higher risk of outliers.

3. Platykurtic (Kurtosis < 3, "Light-Tailed")

   • The distribution has thin tails (fewer extreme values).
   • Data is more spread out and less peaked.
   • Example: Uniform-like distributions.
   • Interpretation: Less likelihood of extreme outliers.
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   • A kurtosis value near 3 suggests normality.
   • A high kurtosis (>3) suggests the presence of outliers.
   • A low kurtosis (<3) suggests a flatter distribution.
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