The amplitude statistical distribution funetion p(l) of the aerosol scattering pulse signals is measured with high resolution through combining the high-speed data acquisition card PCI-9812 and the photoelectric sensor of laser airborne particle counter. The experimental results show that the distribution founction p(l) of the whole signal group and the different pulse width subsets all fit the lognormal distribution with very high precision in the range of amplitude definition (V0,VM) under the condition of big samples, which indicates that the random signal group has a statistical fractal (self-similarity) characteristic. According to the further theoretical results, it is analyzed that function p(l) has a nonlinear scale invariance. Besides, this function shows a geometrical similarity to the power law l-(1-ε) when statistical parameter , where ε<<1.