Functions > Statistics > Descriptive Statistics > Example: Kurtosis and Skewness
Example: Kurtosis and Skewness
Use the kurt and skew functions to compare the shape of a Weibull and a normal distribution.
1. Define and plot the following distributions:
 WD rweibull points 2 kg ND rnorm points 0.87 0.5 kg WH histogram 15
WD kg
NH histogram 15
ND kg
2. Compare the peak of the distributions by calculating the kurtosis of the distributions.
 kurt WD kurt ND
The bins of the histogram account for the slight deviation of the kurtosis of the normal distribution from zero. The kurtosis of the Weibull distribution indicates that it is slightly peaked compared to a normal distribution.
Population kurtosis can be estimated by the following sample kurtosis coefficient:
 kurtosis
WD kg
kurtosis
ND kg
3. Compare the skew of the distributions.
 skew WD skew ND
The Weibull distribution tails off to the right.
Skewness in a population can be estimated by the following sample skewness coefficient:
 skewness
WD kg
skewness
ND kg