The clustering of ultrahigh energy ( > 10 ^ { 20 } eV ) cosmic rays ( UHECR ) suggests that they might be emitted by compact sources .
Statistical analysis ( Dubovsky et al. , 2000 ) estimated the source density .
We extend their analysis to give also the confidence intervals ( CI ) for the source density using a . )
no assumptions on the relationship between clustered and unclustered events ; b . )
nontrivial distributions for the source luminosities and energies ; c. ) the energy dependence of the propagation .
We also 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 } \cdot 10 ^ { -3 } Mpc ^ { -3 } ( on the 68 % confidence level ) .