抄録
It is a well-known fact that the whole information on the statistical property for state variables of a stochastic control system can be derived by finding firstly the multivariate joint probability density function of their variables. Nowadays the actual random data (e.g., the road traffic noise measured by a sound level meter) are measured very often in a digital form at descrete time intervals.
In this paper, we firstly give theoretical consideration on the joint probability function and its joint factorial moments suitable for an actual situation that real experimental data are taken in a form of digital level and as finite numbers. Being compared with the corresponding theories in the case of continuous level distribution, the above theoretical result is characterized by some specific features:
(1) The resulted expression has a difference form instead of differential form. Therefore, the experimental frequency distribution Px(·) can be directly used with keeping its crude numerical form.
(2) When the difference operation is actually done in the practical application, the infinite series type expansion is exactly truncated with a finite number of terms.
(3) As a special case, let the level width tend to 0. The above theory yields the well-known expressions in the continuous level form.
Finally, we have experimentally confirmed the validity of our theory not only by means of digital simulation but also by two kinds of experimentally obtained road traffic noise data in Hiroshima City.
