It has been confirmed that the inner defect of insulator and the perfect diagnosis for aging are closely related to safe electric power transmission system and that the detection of accident and diagnosis technique turn out to be very important issues. But perfect diagnosis is difficult because discharge pattern is irregular. Thus, we investigated discharge pattern using the new distribution statistical models with cross-inked polyethylene(XLPE) specimens. Voltage was applied to power frequency by step method, and calibration of discharge was set to 50 pC. After the voltage was applied, it measured the discharge occurring during 10s. We investigated discharge pattern using the K-means analysis and Weibull function. We also investigated variation of centroid and shape parameter due to variation of voltage. As a result of analyzing K-means, it was confirmed that cluster including many object numbers was formed by the presence of void. And result of Weibull distribution, it was confirmed that shape parameter of discharge varied from 1.28 to 1.62 in no void specimens, and that shape parameter of discharge number varied from 1.28 to 1.62. In the void, shape parameter of discharge varied from 5.66 to 6.43, and shape parameter of discharge number varied from 5.05 to 5.08.