Skewness and kurtosis are two statistical measures used to describe the shape and distribution of data in a dataset.
Skewness refers to the measure of asymmetry in a distribution. It indicates whether the data is distributed symmetrically around its mean. A skewness value of 0 indicates that the data is perfectly symmetric, meaning that the left and right tails of the distribution are equally balanced around the mean. Positive skewness (>0) indicates that the distribution has a longer right tail, meaning there are more extreme values on the right side of the distribution.
Conversely, negative skewness (<0) indicates a longer left tail, with more extreme values on the left side of the distribution. The significance of asymmetry lies in its ability to quantify the departure from a symmetry distribution. It provides insight into the shape and nature of the data distribution, highlighting whether the data is concentrated toward one end of the distribution or spread more evenly across the range of values. A good skewness value depends on the context and the specific requirements of the analysis.
Generally, an skewness value close to 0 (between -0.5 and +0.5) indicates an almost symmetric distribution. This is often considered desirable for many statistical analyzes because it suggests a balanced distribution around the mean. However, the interpretation of asymmetry also depends on the application and the nature of the data.
In some cases, a slightly positive or negative skew may be acceptable or even expected, depending on the domain and underlying characteristics of the data being studied. Kurtosis, on the other hand, measures the "tail" of a distribution, indicating how much of the distribution is concentrated in the tail rather than the center. A kurtosis value of 3 (excess kurtosis of 0) is often used as a reference for a normal distribution. Values greater than 3 indicate heavier tails (leptokurtic distribution), while values less than 3 indicate lighter tails (platykurtic distribution).
A "good" kurtosis value depends on the specific requirements of the analysis. In some cases, a kurtosis near 3 may be preferred, particularly when analyzing financial data or stock returns where heavy tails may indicate higher risk
