The statistical distribution of natural phenomena is of great significance in studying the laws of nature.In order to study the statistical characteristics of a random pulse signal,a random process model is proposed theoretically for better studying of the random law of measured results.Moreover,a simple random pulse signal generation and testing system is designed for studying the counting distributions of three typical objects including particles suspended in the air,standard particles,and background noise.Both normal and lognormal distribution fittings are used for analyzing the experimental results and testified by chi-square distribution fit test and correlation coefficient for comparison.In addition,the statistical laws of three typical objects and the relations between them are discussed in detail.The relation is also the non-integral dimension fractal relation of statistical distributions of different random laser scattering pulse signal groups. The statistical distribution of natural phenomena is of great significance in studying the laws of nature. In order to study the statistical characteristics of a random pulse signal, a random process model is proposed theoretically for better studying of the random law of measured results. Moreover, a simple random pulse signal generation and testing system is designed for studying the counting distributions of three typical objects including particles suspended in the air, standard particles, and background noise. Normal and lognormal distribution fittings are used for analyzing the experimental results and testified by chi-square distribution fit test and correlation coefficient for comparison. In addition, the statistical laws of three typical objects and the relations between them are discussed in detail. The relation is also the non-integral dimension fractal relation of statistical distributions of different random laser scattering pulse signal groups.