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I'm trying to fit a parametric survival model, Exponential, Weibull, Log-normal, Log-logistic. Now I need to use the residuals and hypothesis test to choice the best model for the data. My doubt is:

How I can use the residuals (Cox Snell, Martingal and Deviance) to choice the right model?

What more I can use to check the model fit (AIC, BIC)?

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I'm pretty sure that AIC or BIC are the most commonly used. In cases in which your models are nested, you can use the log-likelihood ratio test or if you go Bayesian, you can use Bayes factors (BF). For details on BF see this post.

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