This paper presents the analysis of partial discharge signals according to the particle states in GIS, for preventing the insulation failure and recognizing the particle states. In this paper, four states of particle (particle on electrode, particle on enclosure, particle on spacer and crossing particle) were simulated. And $Phi$-Q-N distribution of partial discharge signals was analyzed and the statistical operator of the $Phi$-Q distribution was analyzed. As a result, it was found that the states of particle were distinguished by analysis of the $Phi$-Q-N distribution and the statistical operator of the $Phi$-Q distribution.