Calculate Kurtosis in R

Base R does not contain a function that will allow you to calculate kurtosis in R. We will need to use the package “moments” to get the required function.

The kurtosis measure describes the tail of a distribution – how similar are the outlying values of the distribution to the standard normal distribution? The standard normal distribution has a kurtosis of 0.

A negative value for kurtosis indicates a thin tailed distribution; the values of the sample are distributed closer to the median than we would expect for a standard normal distribution. A positive kurtosis value indicates we are dealing with a fat tailed distribution, where extreme outcomes are more common than would be predicted by a standard normal distribution.

Fat-tailed distribution are particular interesting in the social sciences since they can indicate the presence of deeper activity within a social system that is expressed by abrupt shifts to extreme results. Consider the stock market: generally relatively placid, it has the potential for both manias (irrational demand for a stock based on unrealistic expectations) and panics (abrupt declines in a stock price as everyone decides to get out at once). Thus, we can often describe financial markets price movements as fat-tailed. There is the capacity to generate significant extreme values that don’t fall into the standard normal distribution.

# Calculate Kurtosis in R
> install.packages("moments")
> library(moments)
> test <- c(41,34,39,34,34,32,37,32,43,43,24,32)
> kurtosis(test)
[1] 2.724794

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