These wide tails are the result of the chaotic breaks in markets. Benoit Mandelbrot, an IBM mathematician, showed that chaotic systems display distribution curves like the curve in Figure 2. Such distribution curves are not described by the statistics that describe the normal bell curve. These commonly used statistics are called Gaussian statistics. Rather, chaotic systems require the use of a more exotic form of statistics know as Paretian statistics.
Gaussian statistics assume that a price curve is smooth and has no gaps.
Traders know that gaps exist in the price action of markets. Mandelbrot recognized this fact and showed that all chaotic systems have gaps and that they need to be described using Paretian statistics. Quantum Effects in Markets Another behavior of markets is that they show a clear quantum effect. Quantum systems have many balance states. In the structure of the atom, the electrons can exist in several different energy bands.