Negative values in distribution estimation

[mkyron]

Hi SAS Community,

I've been working with some wealth related databases which are well known to follow a pareto distribution. While both pareto and GPD fit the data very well when using proc severity, I overlooked the presence of negative or zero wealth, and therefore a decent amount of people were excluded from the severity procedure. Since I've been using the shape of the distribution to simulate a full population-level sample, I'm hoping to get some insights into procedures or approaches which may be appropriate in capturing both negative wealth and also the extreme outliers that the pareto distributions are good at picking up. A cauchy distribution may be a possibility, although it seems a bit more difficult to estimate in SAS and doesn't fall under proc severity. Any assistance would be greatly appreciated, thankyou

[Ksharp]

Calling @Rick_SAS 

[Rick_SAS]

There is no reason to use the original data scale, which seems to be "dollars above $0" when you fit a distribution. You could use "dollars above negative $1M" instead, or any other threshold value. To use a different reference value, just add that value to every wealth value.  For example, 

Y = $1M + Wealth.

Then fit the distribution of the Y variable, which contains only positive values.

If this worries you, think about measuring elevation in geography. If you measure elevation by using "sea level" as a reference, some places have negative values. But if you choose a different reference point (eg, depth of the Mariana trench), then all elevations become positive.