We present the analysis of a deep colour-magnitude diagram ( CMD ) of NGC 1831 , a rich star cluster in the LMC .
The data were obtained with HST/WFPC2 in the F555W ( \sim V ) and F814W ( \sim I ) filters , reaching m _ { 555 } \sim 25 .
We discuss and apply a method of correcting the CMD for sampling incompleteness and field star contamination .
Efficient use of the CMD data was made by means of direct comparisons of the observed to model CMDs .
The model CMDs are built by an algorithm that generates artificial stars from a single stellar population , characterized by an age , a metallicity , a distance , a reddening value , a present day mass function and a fraction of unresolved binaries .
Photometric uncertainties are empirically determined from the data and incorporated into the models as well .
Statistical techniques are presented and applied as an objective method to assess the compatibility between the model and data CMDs .
By modelling the CMD of the central region in NGC 1831 we infer a metallicity Z = 0.012 , 8.75 \leq \log ( \tau ) \leq 8.80 , 18.54 \leq ( m - M ) _ { 0 } \leq 18.68 and 0.00 \leq E ( B - V ) \leq 0.03 .
For the position dependent PDMF slope ( \alpha = - \mathrm { d } \log \Phi ( M ) / \mathrm { d } \log M ) , we clearly observe the effect of mass segregation in the system : for projected distances R \leq 30 arcsec , \alpha \simeq 1.7 , whereas 2.2 \leq \alpha \leq 2.5 in the outer regions of NGC 1831 .