Asymmetry and Pointing Measures

Asymmetry and Pointing Measures

1. It is a measure that describes how symmetric or skewed a data distribution is.

   • A distribution is symmetric if the observations are evenly distributed around the mean.
   • A distribution is skewed if the observations are more concentrated on one side than the other.

2. Pearson's asymmetry coefficient

   • This coefficient measures the skewness of a distribution around its mean.
   • It is calculated by dividing the difference between the mean and the mode by the standard deviation.

3. A value equal to zero indicates that the distribution is symmetric.

4. A value greater than zero indicates that the distribution is skewed to the right (with a long tail on the right side).

5. A value less than zero indicates that the distribution is skewed to the left (with a long tail on the left side).

6. Fisher asymmetry coefficient

   • It is calculated as the sum of the cubic differences of the observations from the mean, divided by the cube of the standard deviation.
   • This measure is less sensitive to extreme values than the Pearson asymmetry coefficient.

7. kurtosis

   • Mesokurtic
     • when its kurtosis is equal to zero
     • It indicates that its shape is similar to that of a normal distribution.
     • The data are concentrated around the mean in a balanced way
   • Platykurtic
     • when its kurtosis is negative
     • indicating that the distribution is flatter than a normal distribution would be
     • the data has a wider spread, with fewer extreme values.
   • leptokurtic
     • it is considered "peaked", meaning that it has extreme values higher than a normal distribution
     • he data is concentrated closer to the mean and there are a greater number of extreme values.

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