Is the Cullen Frey graph bounded in principle?

Is the Cullen Frey graph bounded in principle?

Your distribution is bounded in principle: that doesn’t appear to bite much as your maximum is well below 100%, but the Cullen-Frey graph (really a variant on a much older graph published by Rhind, but associated with Pearson) includes named distributions that are not so bounded. The biggest deal of all is Why this is being done?

Why was the Pearson distribution used in Cullen and Frey?

It was used long before Cullen and Frey wrote about it (a fact they clearly acknowledge in their text, though their own mention of having seen it in a book written in the late 60s still considerably underestimates its age). The aim of such a plot was to help identify a suitable Pearson distribution.

Can you fit loc.x2 to Cullen Frey graph?

(1) Looking at the Cullen-Frey graph, loc.x2 data cannot be fitted by the families shown in the graph (the blue observation is not even present in the graph). Does it mean that none of these distributions can be used to fit my data?

Is the Cullen-Frey graph relevant to bimodality?

Conversely, if bimodality is real, then (a) you may be able to relate that to subject-matter knowledge (b) none of the distributions named on the Cullen-Frey graph is directly relevant (I exclude the beta too unless U-shapes are relevant to you) (c) skewness and kurtosis can’t capture bimodality directly.

Is the Cullen and Frey plot called a Pearson plot?

This plot used to be commonly called a Pearson plot (it also had several other names), though sometimes with skewness rather than its square being plotted.

Is there skewness and kurtosis in Cullen and Frey?

The Cullen and Frey version of the plot doesn’t show all the Pearson family on the plot; you can’t see from that plot whether the skewness and kurtosis would correspond to that of a Pearson IV or VI distribution because they leave the dividing line off the plot (which corresponds to a shifted and scaled inverse Gamma)