Confidence intervals for the encircled energy fraction and the half-energy width.

The encircled energy fraction and its quantiles, notably the half-energy width, are routinely used to characterize the quality of x-ray optical systems. They are, however, always quoted without a statistical error. We show how nonparametric statistical methods can be used to redress this situation, and we discuss how the knowledge of the statistical error can be used to speed up the characterization efforts for future x-ray observatories.