what model to estimate excess count?


I have values of sales made for 20 months over two months period. The values are recorded as count per month and we have a hunch that the values were under-reported.

I am trying to build a statistical model to estimate the excess count. First of all I know I am to use a longitudinal count model but what I am not certain of is how to compute the excess count from my data using statistical model.

Please any suggestion is highly welcomed.