Geodesic
Asymptotic properties of estimators of parameters of the Weibull distribution
Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part 8, Tome 166 (1988), pp. 9-16

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Properties of the maximum likelihood and moment estimators for the tree-parametric Weibull distribution are investigated under all values of the form parameter $b$. 
@article{ZNSL_1988_166_a1,
     author = {E. O. Balitskaya and L. A. Zolotuhina},
     title = {Asymptotic properties of estimators of parameters of the {Weibull} distribution},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {9--16},
     publisher = {mathdoc},
     volume = {166},
     year = {1988},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1988_166_a1/}
}
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E. O. Balitskaya; L. A. Zolotuhina. Asymptotic properties of estimators of parameters of the Weibull distribution. Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part 8, Tome 166 (1988), pp. 9-16. http://geodesic.mathdoc.fr/item/ZNSL_1988_166_a1/