Kurtosis is a statistical measure, which characterizes the extreme data (outlier) character of a distribution compared with the normal distribution. Positive (excess) kurtosis indicates a distribution that is more outlier-prone than a normal distribution. Negative (excess) kurtosis indicates a distribution that is less outlier-prone than a normal distribution.
Overview
From Wikipedia:
In probability theory and statistics, kurtosis (from Greek: κυρτός, kyrtos or kurtos, meaning "curved, arching") is a measure of the "tailedness" of the probability distribution of a real-valued random variable. In a similar way to the concept of skewness, kurtosis is a descriptor of the shape of a probability distribution and, just as for skewness, there are different ways of quantifying it for a theoretical distribution and corresponding ways of estimating it from a sample from a population. Depending on the particular measure of kurtosis that is used, there are various interpretations of kurtosis, and of how particular measures should be interpreted.
The standard measure of kurtosis, originating with Karl Pearson, is based on a scaled version of the fourth moment of the data or population. This number is related to the tails of the distribution, not its peak;[1] hence, the sometimes-seen characterization as "peakedness" is mistaken. For this measure, higher kurtosis is the result of infrequent extreme deviations (or outliers), as opposed to frequent modestly sized deviations.
Tag usage
Questions on tag kurtosis should be about implementation and programming problems, not about the statistical or theoretical properties of the concept. Consider whether your question might be better suited to Cross Validated, the StackExchange site for statistics, machine learning and data analysis.
