Based on the random process of the photodetector noise signals {Vi}, the different characteristics of the two parts of the random measurementstability constant part and random fluctuation part are analyzed. A new mathematical model of the random noise signal is established. The theoretical analysis shows that the statistical distributions must obey the relationship of nonlinear transform. The distribution laws of the different characteristic quantities in the same random process are studied experimentally, such as, the amplitude of extreme, the amplitudes of the rising edge and falling edge, the interval between extreme points, the difference between adjacent amplitudes, the product value of the quantities and the quotient value of the quantities. And the statistical distribution of these characteristic quantities matches well with the form of the lognormal distribution. From the theoretical and experimental results we can conclude that the lognormal distribution plays an important role in describing the random fluctuation part characteristic of random process.