Statistical Distribution Model of Complicated Random Variables Based on Maximum Entropy Concept

The statistical distribution of random variables are absolutely necessary in many engineering practices, such as reliability analysis, fatigue life test. When building a statistical model, in general a hypothesis is proposed based on statistical data of samples and experience of the engineer, who takes the responsibility. Therefore the hypothesis of the statistical model would be influenced by the opinion of the engineer.

In this paper, based on maximum entropy concept, a statistical model of complicated random variables is presented, and a parameter estimation method of the distribution function is also proposed. Maximum entropy statistical models are used to describe service loads of engine and clutch of a light truck, and rotating speed. The examples show that maximum entropy distribution can fit different frequency distribution.