Kurtosis and Skewness

Skewness

Skewness is the property of a Random Variable which gives us an idea about the shape of probability curve.
The coefficient depends on 3rd because

$$skewness=\frac{{\mu }_3}{{\mu }_2^{3/2}}$$

Depending on the value of coefficient of skewness

• $skewness>0⟹\text{The curve is positively skewed}$
• $skewness<0⟹\text{The curve is Negatively skewed}$

Kurtosis

Its the property of the Random Variable that gives us an idea about the flatness of the probability curve.

$${\beta }_2=\frac{{\mu }_4}{{\mu }_2^2}$$

Depending on the values

• ${\beta }_2=3⟹$ The curve is mesokurtic
• ${\beta }_2<3⟹$ The curve is platykurtic
• ${\beta }_2>3⟹$ The curve is leptokurtic

References

Information

• date: 2025.03.16
• time: 20:44