Appropriate hypothesis test for beta or fractional logistic distributions

Hi! Thanks to previous suggestions I have determined that my bounded data sets are fit well by beta and/or fractional logistic distributions. I am wondering now, what the appropriate hypothesis tests would be for such distributions? I have been using Kruskall-Wallis and the Mann-Whitney/Wilcox ranksum tests, are these appropriate? Does anyone have any other suggestions? Also, I tried a bootstrap test which seemed to give exceedingly liberal p-values and am not comfortable with this...



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How do you know bootstrapping gave liberal p-values? How did you do the boostrap?

You didn't actually tell us what you're testing so. But likelihood ratio tests could work.