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Determining the impact on digital communication systems from electromagnetic interference often requires complex analyses or computations. Therefore, there is a need for low-complexity approximate methods suitable in computer-based tools for intersystem interference analyses. A commonly used approximation is to treat the interference as additive white Gaussian noise (AWGN), when estimating the resulting bit error probability (BEP). However, the validity of this approximation varies for different types of interference. Previously, it has been shown that higher-order statistics (HOS) can be used to estimate the quality of the AWGN-approximation for periodic pulsed interference with fixed amplitude. In this paper, we show that it is possible to use HOS to estimate the quality of the AWGN-approximation for a more general pulsed interference with random amplitude and arrival time. The results open the possibility to use HOS as a quality measure of the resulting BEP when using low-complexity approximate methods in computer-based tools.