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Skewness-Kurtosis Plot
A skewness-kurtosis plot indicates the range of skewness and kurtosis values a distribution can fit. An example is shown below:
Two-parameter distributions like the normal distribution are represented by a single point. Three parameters distributions like the lognormal distribution are represented by a curve. Four parameter distributions like the beta distribution are represented by a shaded region.
At the bottom of the plot is a gray shaded region called the impossible region. No distributions can fall into this region.
The skewness-kurtosis plot can be used in many ways:
Locate the point on the plot that corresponds to a set of data and see which distributions are nearby and might fit the data.
See which distributions are close to each other. For example, the exponential distribution is at the point where the gamma and Weibull distributions intersect and is a special case of both distributions. Another example is that the normal distribution is on the curve of the lognormal distribution. The lognormal distribution limits to the normal distribution as the skewness goes to zero.
See the relationships between distributions. For example, the lognormal distribution's curve is above the gamma distribution's curve. This means that for the same skewness, the lognormal distribution has a higher kurtosis (heavier tails) than the gamma distribution.