Recently , the High Resolution Fly ’ s Eye ( HiRes ) experiment claims that there is no small scale anisotropy in the arrival distribution of ultra-high energy cosmic rays ( UHECRs ) above E > 10 ^ { 19 } eV contrary to the Akeno Giant Air Shower Array ( AGASA ) observation .
In this paper , we discuss the statistical significance of this discrepancy between the two experiments .
We calculate arrival distribution of UHECRs above 10 ^ { 19 } eV predicted by the source models constructed using the Optical Redshift Survey galaxy sample .
We apply the new method developed by us for calculating arrival distribution in the presence of the galactic magnetic field .
The great advantage of this method is that it enables us to calculate UHECR arrival distribution with lower energy ( \sim 10 ^ { 19 } eV ) than previous studies within reasonable time by following only the trajectories of UHECRs actually reaching the earth .
It has been realized that the small scale anisotropy observed by the AGASA can be explained with the source number density \sim 10 ^ { -5 \sim - 6 } Mpc ^ { -3 } assuming weak extragalactic magnetic field ( B \leq 1 nG ) .
We find that the predicted small scale anisotropy for this source number density is also consistent with the current HiRes data .
We thus conclude that the statement by the HiRes experiment that they do not find small scale anisotropy in UHECR arrival distribution is not statistically significant at present .
We also show future prospect of determining the source number density with increasing amount of observed data .