Discriminating between the Weibull and log‐normal distributions

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Is Weibull distribution the most appropriate statistical strength distribution for brittle materials (2009, background): “(20) Now between the two families F and G choose family F if χ(2)f,data < χ(2)g,data and choose family G otherwise.”
On the comparison of Fisher information of the Weibull and GE distributions (2006, methodology): “Similarly, if we frame this model discrimination problem as a testing of hypothesis problem (see Kundu and Manglick [12]), then also we can not reject any of the null hypotheses.”