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Several old and new density estimators may have good theoretical performance, but are hampered by not being bona fide densities; they may be negative in certain regions or may not integrate to 1. One can therefore not simulate from them, for example. This paper develops general modification methods that turn any density estimator into one which is a bona fide density, and which is always better in performance under one set of conditions and arbitrarily close in performance under a complementary set of conditions. This improvement-for-free procedure can, in particular, be applied for higher-order kernel estimators, classes of modern "h"-super-4 bias kernel type estimators, superkernel estimators, the sinc kernel estimator, the "k"-NN estimator, orthogonal expansion estimators, and for various recently developed semi-parametric density estimators. Copyright Board of the Foundation of the Scandinavian Journal of Statistics 2003..

A new statistical method for estimating the orientation distribution of fibres in a fibre process is suggested where the process is observed in the form of a degraded digital greyscale image. The method is based on line transect sampling of the image in a few fixed directions. A well-known method based on stereology is available if the intersections between the transects and fibres can be counted. We extend this to the case where, instead of the intersection points, only scaled variograms of grey levels along the transects are observed. The nonlinear estimation equations for a parametric orientation distribution as well as a numerical algorithm are given. The method is illustrated by a real-world example and simulated examples where the elliptic orientation distribution is applied. In its simplicity, the new approach is intended for industrial on-line estimation of fibre orientation in disordered fibrous materials.