Stereological estimation of particle size distributions

The corpuscle problem of Wicksell is discussed. We give a numerical quadrature of Gauss.Chebyshev type for Wicksell's integral equation which combines a size distribution of discs on a sectional plane with that of spheres. We also give an estimation procedure of three-dimensional size distributions based on this quadrature and examine its theoretical properties. In practice, we need a smoothing technique for empirical distribution functions before applying this estimator. Simulation results are given. Our idea also is applied to the thick section case and an analysis of microscopic data is given.