In reply to Ksharp.

Thanks for writing. You have an excellent memory! My previous blog post (from 2014) used linear interpolation for a set of published quantiles to estimate the CDF. Here is a comparison of the two methods:
1. The linear interpolation method always works, regardless of the number of quantiles or their values.
2. If you simulate from the linear interpolation model, the simulated data will always be within the range [min, max], where min and max are the published values for the minimum and maximum values of the original data.
3. However, the PDF is the derivative of the CDF, so the PDF is piecewise constant and is discontinuous at the published values. Thus, it is not a good model for a continuous data-generating process.
4. The metalog method might not be feasible. It depends on the values of the published quantiles.
5. The metalog model will not exactly match the published quantiles exactly.
6. Depending on the order of the model, you could obtain modes for the model PDF that are not present in the original data. A low order model will always be unimodal. A high order model will have multiple modes. Without access to the original data, it is hard to know which order to choose for the model.

So, I guess my response is that you shouldn't discard the linear interpolation method. The metalog distribution has some advantages, but some weaknesses as well.