The comparison by simulation of solutions of Wicksell's corpuscle problem

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Abstract
SUMMARY: In this paper six distribution‐free (nonparametric) stereological methods for the solution of Wicksell's corpuscle problem—i.e. the determination of the distribution of diameters of spheres embedded in an opaque specimen from the diameters of their profiles on plane sections—are compared as regards their numerical stability, sensitivity to underlying distributions and certain error criteria. The study is based on the results of simulation studies for several types of distribution (one‐point, normal, exponential, logarithmic normal) of sphere diameters. Recommendations are suggested for the choice of methods, sample size and the optimal number of classes for grouping sample data.