Some problems in Hadwiger fertility graduation

Abstract
The Hadwiger function has been recommended for the analytic graduation of fertility curves. In its original parametrization, this graduating function has some rather problematic aspects in terms of parameter identifiability and interpretability. This can be remedied by a suitable reparametrization. However, a second practical identification problem arises insofar as the curves of the Hadwiger density and the gamma density with similar parameter values turn out to be virtually interchangeable in a number of numerical examples. Our impression is that the Hadwiger density is a bit more flexible than the gamma density. In this respect, therefore, the Hadwiger density seems to have a slight edge on the gamma density. These are the main concerns of this paper. In addition some findings are presented on methods of parameter estimation in current use. Moment type estimators turn out to be seriously inconsistent in several actual cases, and their replacement by minimum chi-square estimators is recommended.

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