A new construction of the Gaussian distribution is introduced and proven. The procedure consists of using fractal interpolating functions, with graphs having increasing fractal dimensions, to ...

All sorts of physical processes in this analog world exhibit some degree of randomness. Think of noise, for example. Many noisy processes are described by Gaussian probability distributions. We should ...

The “tail” of a particle size distribution references the particles that are several standard deviations removed from the mean of the standard Gaussian distribution. Figure 1 demonstrates the ...

Appropriate modeling of time-varying dependencies is very important for quantifying financial risk, such as the risk associated with a portfolio of financial assets. Most of the papers analyzing ...

A random distribution of events that is graphed as the famous "bell-shaped curve." It is used to represent a normal or statistically probable outcome and shows most samples falling closer to the mean ...

It may be misleading to estimate value-at-risk (VAR) or other risk measures assuming normally distributed innovations in a model for a heteroscedastic financial return series. Using the t-distribution ...