Hello Everyone !!

I have been trying to estimate the parameters of the kumaraswamy(alpha ,beta) distribution using 5 different methods (MLE,MOM ,PWM ,self determined PWM,POME )
In the notebook i attached a detailed explanation of the POME method ,my problem is that i am not getting estimates that are reasonable at all ...i have tried to restrict the domain of the dist by truncating the data but the problem still holds ..i have a paper of real life data and estimates were obtained using this method ,so can anyone please have a look at the simulation part and suggest solutions.
My goal is to simulate 1000 data sets with 20 sample size each and the true values of alpha and beta are 2