I found this document that describes actuarial credibility.
In the document, they describe the basic formula for calculating credibility weighted estimates as:
where Z is the credibility assigned to the observation and 1 - Z is the complement of credibility.
The standard for full credibility of aggregate losses, pure premiums, and loss ratios is:
where depends on the initial P and k values that are selected.
Finally, in order to determine the value of Z, it is necessary to divide the number of claims for the volume of data () by the standard for full credibility (
) and square the result:
My question is can I apply this credibility rule to the Census Bureau's PUMS data (specifically, averages such as the average household income or aggregate totals such as the total number of vehicles)?
For those unfamiliar, in the PUMS data, each observation has a household income associated with it and is weighted with a certain WGTP. Thus, average household income could be computed like such:
In the above example, I was wondering if I could treat the average household income measure the same way I would treat a pure premium or loss ratio. Is this mathematically valid or is there something I'm missing?
Thanks!
Edit: posted images for formulas