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 ...

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 ...

I have been thinking about Brownian motion a lot lately.Random walks, Gaussian distributions, Ito calculus, stochastic differential equations, and diffusion equations.As I researched these, a certain ...

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 ...

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 ...

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 ...