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A standard problem in the study of star clusters and galaxies is estimation of a number density profile $\nu(r)$ given measured positions, on the plane of the sky, of a large set of objects. The most common approach to this problem is a parametric one: the number counts are binned in projected position and fit to some ad hoc function $\Sigma(R;\theta)$, where the $\theta$ are a set of parameters that are varied to achieve the optimum fit. Here we adapt some existing nonparametric techniques to the problem of estimating $\Sigma(R)$ and $\nu(r)$ from discrete samples. The algorithms require no binning and are able to cope with the amplification of errors associated with Abel deconvolution. We apply the algorithms to the determination of the density profiles of the globular cluster M15, and the Coma galaxy cluster.
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