Family of Distributions

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Family of Distributions

A family of distributions is several distributions combined so that they cover a well define region in a skewness-kurtosis plot. For example, the lognormal family of distributions includes the lognormal, negative lognormal and normal distributions. This allows the family to fit all possible average, standard deviation and skewness values. It appears as a curve in the skewness-kurtosis plot. The lognormal, negative lognormal and normal distributions are distinct distributions because they have different density and distribution functions.

There are two families that allows one to fit all possible average, standard deviation, skewness and kurtosis values (excluding the impossible region): Johnson, combining 3 distributions, and Pearson, combining 7 distributions.