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The likelihood ratio is the ratio of the likelihoods of two models (or a null and alternative parameter value within a single model), which may be used to compare or test the models. If either model is not fully specified then its maximum likelihood over all free parameters is used - this is sometimes called a generalized likelihood ratio.
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Using AIC vs Likelihood Ratio test for comparing Lognormal and Powerlaw distributions
I am interested in comparing whether a lognormal or a power law are a better fit for a given set of data. Both distributions have been fit using MLE, with $x_{min}$ determined using KS-minimization a …