We consider the following discrete time inventory model: The sizes of demand are independent restricted to the integers random variables with common distribution {bi,i= 1,2,…}. The times between demands are positive independent random variables with common absolute-continuous distribution functionF(t). The replenishment policy is of the modified (r, Q)-type and the lead times of orders are independent exponential distributed random variables. Unfilled demands are lost. We obtain the limit distribution of the stock on hand and compute this distribution for the special example.