Basically I need to make up a PDF that is skewed enough that it wont really fit the CLT unless I have a large number of observations. I have no idea how to just make one up (I cant use anything with a name like Chi squared, poisson, etc.)

I know obviously the properties of a PDF (it must have all positive values, the integral has to equal 1, etc.)

I just need some help on how to start.

Thanks in advance