Skewness and kurtosis in R are available in the moments package (to install an R package, click here), and these are:
- Skewness – skewness
- Kurtosis – kurtosis
Interpretation: The skewness here is -0.01565162. This value implies that the distribution of the data is slightly skewed to the left or negatively skewed. It is skewed to the left because the computed value is negative, and is slightly, because the value is close to zero. For the kurtosis, we have 2.301051 implying that the distribution of the data is platykurtic, since the computed value is less than 3.
Graphical illustration of the data is in Figure 1.
|Figure 1. Histogram of the Time Elapsed|
Example 2. Simulate 10000 samples from a normal distribution with mean 55, and standard deviation 4.5, then compute and interpret for the skewness and kurtosis, and plot the histogram.
Interpretation: The skewness of the simulated data is -0.008525844. This concludes that the data are close to bell shape but slightly skewed to the left. The computed kurtosis is 2.96577, which means the data is mesokurtic. Figure 2 is the histogram of the simulated data with empirical PDF.
|Figure 2. Histogram of the Simulated Data|