  Dynamical systems in nature exhibit selfsimilar fractal fluctuations and the
corresponding power spectra follow inverse power law form signifying long-range
space-time correlations identified as self-organized criticality. The physics
of self-organized criticality is not yet identified. The Gaussian probability
distribution used widely for analysis and description of large data sets
underestimates the probabilities of occurrence of extreme events such as stock
market crashes, earthquakes, heavy rainfall, etc. The assumptions underlying
the normal distribution such as fixed mean and standard deviation, independence
of data, are not valid for real world fractal data sets exhibiting a scale-free
power law distribution with fat tails. A general systems theory for fractals
visualizes the emergence of successively larger scale fluctuations to result
from the space-time integration of enclosed smaller scale fluctuations. The
model predicts a universal inverse power law incorporating the golden mean for
fractal fluctuations and for the corresponding power spectra, i.e., the
variance spectrum represents the probabilities, a signature of quantum systems.
Fractal fluctuations therefore exhibit quantum-like chaos. The model predicted
inverse power law is very close to the Gaussian distribution for small-scale
fluctuations, but exhibits a fat long tail for large-scale fluctuations.
Extensive data sets of Dow Jones index, Human DNA, Takifugu rubripes (Puffer
fish) DNA are analysed to show that the space/time data sets are close to the
model predicted power law distribution.
