Accumulated Basin Storage (ABS) which is an estimate of soil moisture levels in a river basin is used to quantify agricultural droughts. The relevance of ABS to agricultural droughts is investigated by means of its correlation with crop yield within the basin. It is observed that crop yield is more strongly correlated with ABS than with other parameters such as precipitation and runoff and thus the ABS will be the better drought estimating parameter. In the method, agricultural drought is related to soil moisture deficit, when the ABS falls below a reference base level. The ABS is a random variable and its annual sequence is a random time series with a specific correlation structure. A statistical experimental method of generating a large number of time series samples can be used to estimate probability distributions of characteristic drought variables. The drought variables considered here are the number of droughts occurring in an given time interval, the magnitude of soil moisture deficits, the rate at which soil moisture deficit porgresses (or drought intensity), and the duration of drought events. Also, the largest drought deficit, intensity and longest durations are considered. The theory of the maximum of a random number of random variables is used to interprete the experimental results. This approach is based on the assumption that drought is independent identically distributed random variable whose occurrence follows the Poisson probablility law. These assumptions are checked and found to be satisfied. The comparison between the experimental and theoretical results are shown graphically and statistical tests were conducted to show their goodness of fit.