Procedure 10: Create the Skewness and Kurtosis statistics
It can be observed from procedure 55 that the histogram has a severe lean towards the axis, which would be described as being positively skewed. The positive skew deviating from the shape expected of a normal distribution would be cause mistrust of the standard deviation that was created in procedure 61. Two useful statistics and functions for assessing the extent to which a distribution deviates from the normal distribution is skewness() measuring the lean towards and away from the y axis and kurtosis() measuring how tall or squashed the distribution is.
The functions skewness() and kurtosis() do not exist in the base R packages rather they are available in a package called moments. It follows that the moments package need be installed then loaded. Search for and install the package moments via RStudio:
Click the Install button to run the installation instruction to console:
Load the library moments by typing into the script window:
library(moments)
Run the line of script to console:
Firstly, in the quest to appraise the extent to which the vector leans towards or away from the axis, type:
skewness(AAPL$Interim_Close)
Run the line of script to console:
It can be observed that there is a positive value returned, indicating that there is indeed lean and owing to it being positive, that the lean is towards the y axis (which is of course what was visually observed in procedure 55). Secondly to understand if the distribution is tall or squat, verify the kurtosis by typing:
kurtosis(AAPL$Interim_Close)
Run the line of script to console:
The kurtosis is a difficult statistic to make sense of and in many respects the skewness is a more useful statistic. To make an assessment of the shape of the distribution, typically, all summary statistics need to be considered:
