Values and Application of Skewness and Kurtosis for a Normal Distribution

Skewness is a measure of the lack of symmetry. A dataset is symmetric when the centre point is same from both left and right. The skewness is zero for a normal distribution. For any symmetric data the skewness should be near to zero. 

Kurtosis measures if the data distribution is heavy tailed or light tailed in relation to a normal distribution. The data set is heavy tailed if it has high kurtosis and the data set is light tailed ifit has low kurtosis. Positive kurtosis means heavy tailed distribution and low tailed distribution means negative kurtosis. 

Values of Skewness 

If the distribution of values is not symmetrical then it is said to be “skewed”. A skewness value that is greater than 1 or less than -1 states a high skewness distribution. A value between 0.5 and 1 or -0.5 and -1 indicates moderate skewness distribution. A value between -0.5 and 0.5 demonstrates that the is fairly symmetrical distribution. There are three types of skewness: Right skew which is also called positive skew, left skew also known as negative skew, and Zero skew.

Application of Skewness 

i. Skewness provides an idea about the direction of outliers whether it is right side or left sideof the distribution. 

ii. It  measures the symmetry of the distribution. 

iii. Skewness is useful in obtaining approximate probabilities and quantiles of distributions.

iv. It is used for better examining the likelihood of events falling in the tails of a probability distribution.

Values of Kurtosis 

The normal distribution of kurtosis is 3. This is observed in a symmetric distribution. Adistribution greater than three means positive kurtosis. The value of positive kurtosis liesfrom 1 to infinity. A kurtosis less than three indicates a negative kurtosis. The value will range from -2 to infinity in negative kurtosis. The greater the value of kurtosis, the higher isthe peak. There are three types of kurtosis which are mesokurtic, leptokurtic, and platykurtic.Distributions with medium tails or medium kurtosis are mesokurtic, distributions with low kurtosis or thin tails are platykurtic, and distributions fat tails or high kurtosis are leptokurtic.

Application of Kurtosis

i. Kurtosis is useful in measuring if there is a problem with outliers in a data set.

ii. It is used for measuring financial risk in finance such as the risk an investment carries.

iii. Kurtosis determines the heaviness of the distribution tails.