We study the accuracy and systematic error of inference of massive halo objects ’ ( MHO or ‘ Macho ’ ) mass function from microlensing events observed in the direction of Large Magellanic Cloud .
Assuming the spatial distribution and kinematics of the objects are known , the slope and the range of the MHO mass function ( modeled here by a simple power law ) will be possible to determine from 100-1000 detected events if the slope is in the range -2.5 \raise 1.29 pt \hbox { $ < $ \kern - 7.5 pt \lower 4.3 pt \hbox { $ \sim$ } } \alpha % \raise 1.29 pt \hbox { $ < $ \kern - 7.5 pt \lower 4.3 pt \hbox { $ \sim$ } } -0.5 , with the statistical errors reaching their minima at \alpha = -1.5 .
Outside this range the errors grow rapidly making the inference difficult even at very large numbers of events ( N \approx 10000 ) .
On the other hand , the average mass of the MHO ’ s will be determined to better than about 30 % accuracy from N \approx 100 events for any slope .
Overall , we find that the accuracy of inference at fixed N will not be strongly affected by the presently available event duration-dependent detection efficiencies if the typical MHO masses are in the range ( order of magnitude 0.1 M _ { \odot } ) indicated by the events detected so far .

We also estimate the effects of the uncertainty of the massive objects ’ spatial distribution and kinematics on the determination of their mass function .
The massive objects ’ halo models considered are all spherical but we allow for various density profiles and a radius-dependent , anisotropic velocity dispersion .
We find that while the mass function slope and range ( i.e. , the ‘ shape ’ ) are weakly affected for -2 \raise 1.29 pt \hbox { $ < $ \kern - 7.5 pt \lower 4.3 pt \hbox { $ \sim$ } } \alpha % \raise 1.29 pt \hbox { $ < $ \kern - 7.5 pt \lower 4.3 pt \hbox { $ \sim$ } } 0 , the error in the average mass due to the halo structure uncertainties could be reduced to less than about 50 % only through the detection of about 1000 or more events .
Reliable estimates of the halo structure itself [ density profile and ( anisotropic ) velocity dispersion profile ] can start only at very large numbers of detections ( N \raise 1.29 pt \hbox { $ > $ \kern - 7.5 pt \lower 4.3 pt \hbox { $ \sim$ } } 10000 ) .