Weibull distributions when the shape parameter is defined. (Q5941106)

The Weibull distribution, depending on parameters of location, scale, and shape, is often useful as a model for fracture data sets. If the location parameter is to be estimated then we have shown that maximum likelihood methods are not recommended. In the data set considered here the shape parameter is known to lie between 2 and 3 or so. We therefore studied the two-parameter model for which the shape parameter is known, or has a probability structure. Simple moment estimators are used and some moments of these are studied and verified by simulation.