Bangladesh, a tropical low-lying region, is stranded between the Bay of Bengal in the south and the Himalayas in the north. The unique characteristics allow receiving huge rainfall, in particular, in the monsoon season. The physical phenomena such as the Bay of Bengal, the Himalayas and the monsoon season dominate the extreme rainfall pattern in Bangladesh. However, how to include that information to good effect in the estimation of extreme rainfall at ungauged locations is yet to be investigated. The objective of this work is to examine the information that needs to be included in the estimation of extreme rainfall in such regions. The approach that permits parameters of an extreme value distribution to vary spatially is used to determine the probability model. The methodology, subsequently, authorizes the frequency analysis to be performed at ungauged conditions. The geostatistical technique in the form of kriging with external drift (KED) which has the ability to take secondary information is used to produce spatial maps of the parameters. This study primarily assessed KED interpolation scheme and its ability to accurately predict the model parameters. The scheme was compared against the more widely used ordinary kriging (OK) model. The cross- validation was used to find the robust scheme for each parameter. Annual maximum daily rainfall data from 34 measuring stations were used for the assessment. The KED with the covariate annual mean monsoon rainfall (AMMR) appears to be the best model for location parameter. However, for the scale and shape parameter the KED models were unable to score past the OK model. The availability of parameter maps allows the estimation of extreme rainfall at locations where rainfall records were absent and offers a much better elucidation than the traditional at-site quantile based interpolation. Overall, the inclusion of monsoon rainfall and spatial information are deemed necessary for the estimation of extreme rainfall at ungauged locations in a low-lying monsoon region.