SMOOTHED NONPARAMETRIC-ESTIMATION OF THE LUMINOSITY FUNCTION FOR FLUX-LIMITED SAMPLES

A smoothed nonparametric method for estimating the intrinsic distribut ion of truncated sample data is described. This method determines both the cumulative and differential forms of the distribution, and it doe s not suffer from the numerical fluctuations associated with histogram distributions commonly used to describe such data. Variation of a sin gle smoothing parameter provides a convenient means of error estimatio n and allows for differentiation between random fluctuations and subtl e features which may exist in the parent distribution. The smoothing m ethod is useful for obtaining distribution functions for flux or magni tude-limited astronomical data, and as an example, we calculate the sm oothed luminosity function of a flux-limited sample of approximately 5 00 quasars.