I'm fairly new to statistics (a handful of beginner-level Uni courses) and was wondering about sampling from unknown distributions. Specifically, if you have no idea about the underlying distribution, is there any way to "guarantee" that you get a representative sample?
Example to illustrate: say you're trying to figure out the global distribution of wealth. For any given individual, you can somehow find out their exact wealth; but you can't "sample" every single person on Earth. So, let's say you sample n = 1000 people at random.
If your sample didn't include Bill Gates, you might think there are no billionaires in existence.
If you sample did include Bill Gates, you might think billionaires are more common than they actually are.
In either case, you can't really tell how common or rare billionaires are; you may not be even able to tell whether any exist at all.
Does a better sampling mechanism exist for a case like this?
How would you tell a priori what sampling procedure to use (and how many samples are needed)?
It seems to me that you might have to "sample" a huge percentage of the population to know, with anything approaching reasonable certainty, how common or rare billionaires are on the planet, and that this is due to the underlying distribution being a bit difficult to work with.