Hello everyone,

for my master's thesis I am working with a survey dataset on wealth distribution where I am re-estimating the top tail of the distribution, i.e. the richest households. Since I assume that my wealth data follows a Pareto distribution, I need to find xmin, e.g. the right scale parameter in order to identify the cut-off-point. I have chosen the upper 10 percentiles of my wealth variable for possible xmins. For these 10 percentiles I calculated the respective CCDFs and estimated the 10 possible shape parameters "alpha".

I now want to perform a Kolgomorov-Smirnov test to identify the correct xmin using the p-values. If I understand the test correctly, it is primarily intended to test non-normal distributions. The assumed empirical (in my case Pareto) distribution is compared to a hypothetical distribution and the distance between both is calculated. If H0 cannot be rejected, the hypothetical fits the empirical model.

"Help ksmirnov" says:
Code:
ksmirnov varname = exp [if] [in]
where varname is the variable whose distribution is being tested, and exp must evaluate to the corresponding (theoretical) cumulative. In the example, they test for normal distribution and do so by putting in the function "normal(mean/sd)" for exp. Here's where I'm stuck and I think I'm lacking some theoretical background. I assumed that I would use a pareto function in the same way. And I would do that for all 10 percentiles of my wealth distribution. However, Stata only offers "rpareto", whereby nothing useful comes up. What do I have to put in for exp to test my data for pareto distribution? Do I have to calculate a hypothetical Pareto distribution to test my data against? If so, how would I do that?

Thank you and kind regards
Moritz