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The kurtosis statistic is an effective detector of pulsed sinusoidal radio frequency interference (RFI) in a microwave radiometer, but it fails to detect RFI when the pulsed sinusoid is present for exactly half of the integration period. That is, the kurtosis is blind at an RFI duty cycle of 50%. In this letter, we explore the possibilities of using a higher order statistic to eliminate this detection blind spot in the kurtosis statistic and to improve RFI detection performance. The sixth-order statistic does have sensitivity at an RFI duty cycle of 50%, but sensitivity is relatively low. In addition, it has a sensitivity comparable with the kurtosis for short duty cycle RFI, under certain circumstances.