The 3-parameter Burr distribution has been a mainstay of SSD modelling for many years. Indeed, the name is embedded in the Australian and New Zealand governments’ approved software tool Burrlioz which has been in use for over 20 years. As the research community moves to address some well-know issues with SSD model-fitting, it has become increasingly obvious to a number of us that the 3-parameter Burr family is inherently ‘unstable’ insofar as the iterative MLE computations often fail to converge or converge to multiple optima (due to a flat likelihood profile). We suspect this issue is related to the high collinearity between estimates of the two shape parameters in the Burr III distribution.
So, the issue we’re now grappling with is: do we stick with the Burr and try to sort out the numerical issues (if that’s possible); or do we look for alternative, better-behaved distributions?
I’m leaning towards the latter. Accordingly I offer a ‘new’ 3-parameter distribution as a candidate SSD – the gamma-generated logistic (ggLogis).
I’ve written a brief technical note which can be accessed at: https://bit.ly/30h6Gz8 .
Thoughts welcome!
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