Statistical characteristics of the discrete dynamical system in the orbit-product series, which can be generated from the logistic and the Ulam=von Neumann mapping, have been studied by a computer simulation. The return plots of the series show the so-called 'camel's hump shape", and its patterns just accord with the analytical results using the envelope. The shape of the histogram for the values composing the orbit-product series shows the power distribution and the probability density function can be found out experimentally. These orbit-product series do not suit with the pseudo random numbers. However it is suggested that the pseudo normal random numbers for practical use can be obtained by the average operation after the time phase operation, based on the Central Limit Theorem.
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