Based On The Logarithmic Normal Distribution Random Signal Statistical Characteristics

This paper focuses on the characteristics of a kind of random process which obey the laws of the lognormal distribution and try to explain the reason for random signals following lognormal distribution.First, this paper attempts to establish a mathematical model that stand for the characteristics of the random process which obey the lognormal distribution, the mathematical model can be used to describe the random process by analyzing the relationship between the output of stochastic processes and the random effect factors. By analyzing the random phenomena that obey the laws of the lognormal distribution of different fields, and the reason for the random variation of the random variable of the random process, to establish a mathematical model between the variance of the random variable of the random process and the variance of random effect factors.Then analyze the mathematical model of the random process, find it apply to the random system that a random process has at least three random effect factors. Discuss the statistical mean of the calculation method, obtain the geometric mean applies to random process discussed in this paper. And geometric mean theoretically constrained random process to obey lognormal distribution.Finally, this paper takes the OPC instrument as a typical random system, analyze the relationship between the system output signal and the effect factors, indicating that the system meets the established random process model, taking the random noise pulse signal of the system as the research object, prove that the geometric mean is the best mean calculation for the random process that obey the lognormal distribution. Census the amplitude of the OPC instrument random noise pulse signal, the scattered light pulse signal of the suspended particles and standard particle, and the lognormal distribution that its independent variable is natural number can fit these three different random signals. Compare the values of statistical skewness of the three signals, finding the values of the skewness effect by the effect factors which can show that factors of the random signal are the main reason that causing stochastic processes obey the lognormal distribution.