Skewness

Skewness of a Distribution

In this section, the concept of skewness in a distribution is discussed, highlighting how skewness can be represented by the third central moment of a distribution.

Understanding Skewness

• Skewness refers to the asymmetry in a distribution, with positively skewed distributions having a long positive tail.

• Positively skewed distributions are characterized by an extended positive tail towards the x-direction.

• Skewness can be quantified using the expectation of (x - mean)^3.

• This calculation helps determine whether a variable is positively skewed or symmetric.

• For symmetric distributions, the average value of (x - mean)^3 is zero.

• Symmetric distributions exhibit no skewness as the average value is centered around zero.

Calculating Skewness

• Skewness can be measured by dividing the third central moment by sigma squared and raising it to power three over two.