[igraph] how to choose xmin in power.law.fit {igraph}

[sarai shai]

Hello. 

I am trying to find probability density distribution that best fits my data. Therefore, I am trying to fit several models (like gamma, pareto, log-normal, ...) and then choose the best one using Akaike Information Criterion (AIC). 

In order to fit power-law distribution I am using power.law.fit {igraph}. My problem is how to choose xmin. I know that as a default R choosing xmin to be the smallest value in the data, but I am afraid that such a selection for xmin will give the power-law advantage on all the other models, since all the others defined on (0, infinity) and the biggest fitting error is obtained in the tails. So, here are my questions: 

1. How can I choose the best xmin such that the model selection will not be biased in the favour of power-law? 
2. How can I make sure that the lower bound I have chose is good enough. 

Thank you very much in advance, 
Saray Shai