After sampling the particle collision voltage signal in particle impact noise detection (PIND) test, the change trend of the parameters corresponding to the sampled data after the sample size increased was studied. It shows that the average value of ＞20mV sampling values tends to be stable, reflecting a certain statistical law. Considering the randomness of the particle collision process and the velocity attenuation trend, the hypothesis that the velocity change process can be regarded as a Poisson process in the velocity space was proposed, and the conjecture that the sampling value ＞20mV conforms to the exponential distribution was reached. For the combination of multiple particle types, particle positions and test frequencies, the probability density of exponential distribution obtained from this conjecture is consistent with the probability density obtained from sampled data, indicating that the hypothesis and its conjecture are valid, and the relationship between λ of exponential distribution and various factors is discussed. The obtained statistical model and the method used are instructive for the study of particle collision process and the characteristics of remainder.