  The normal distribution is used as a unified probability distribution,
however, our researcher found that it is not good agreed with the real-life
dynamical system's data. We collected and analyzed representative naturally
occurring data series (e.g., the earth environment, sunspots, brain waves,
electrocardiograms, some cases are classic chaos systems and social
activities). It is found that the probability density functions (PDFs) of first
or higher order differences for these datasets are consistently fat-tailed
bell-shaped curves, and their associated cumulative distribution functions
(CDFs) are consistently S-shaped when compared to the near-straight line of the
normal distribution CDF. It is proved that this profile is not because of
numerical or measure error, and the t-distribution is a good approximation.
This kind of PDF/CDF is a universal phenomenon for independent time and space
series data, which will make researchers to reconsider some hypotheses about
stochastic dynamical models such as Wiener process, and therefore merits
investigation.
