Given word-level statistics, namely mean, standard deviation, and lag-one temporal correlation of input data, we estimate the bit-level crosstalk probability on a system bus using a non-enumerative statistical approach. We introduce a sampling technique for fast evaluation of integrals during the estimation process. We had proposed two techniques previously - (a) a stream-based estimator that counts crosstalk events on a bus; and (b) a statistical enumeration technique that enumerates crosstalk-producing values on a bus and computes their occurrence probability. Both these techniques suffer from exponential time complexity with respect to the bus-width. In this work, we propose a statistical non-enumerative technique that has linear time complexity with respect to the bus-width. We achieve the linear complexity by resorting to: (1) manipulating the data stream to make the crosstalk-producing values contiguous and (2) sampling the distribution function and storing it as a lookup table. Experimental results for data streams from different data environments are presented, compared against the stream-based approach. Average errors of less than 12% are obtained for bus-widths ranging from 8b to 32b.