  The clustering of ultra high energy (above 10^20 eV) cosmic rays (UHECR)
suggests that they might be emitted by compact sources. Statistical analysis of
Dubovsky et al. (Phys. Rev. Lett. 85 (2000) 1154) estimated the source density.
We extend their analysis to give also the confidence intervals for the number
of sources using a.) no assumptions on the relationship between clustered and
unclustered events; b.) nontrivial distributions for the source intensities and
energies; c.) the energy dependence of the propagation. We determine the
probability that a proton created at a distance r with energy E arrives at
earth above a threshold E_c. Using this function one can determine the observed
spectrum just by one numerical integration for any injection spectrum. The
observed 14 UHECR events above 10^20 eV with one doublet gives for the source
densities 180_-165^+2730*10^-3 Mpc^-3 (on the 68% confidence level). We present
detailed results for future experiments with larger UHECRs statistics.
