# Statistics

Pink noise. Within the scientific literature the term pink noise is sometimes used a little more loosely to refer to any noise with a power spectral density of the form where f is frequency and 0 < α < 2, with exponent α usually close to 1.

These pink -like noises occur widely in nature and are a source of considerable interest in many fields. The distinction between the noises with α near 1 and those with a broad range of α approximately corresponds to a much more basic distinction. The former (narrow sense) generally come from condensed matter systems in quasi-equilibrium, as discussed below.[2] The latter (broader sense) generally correspond to wide range of non-equilibrium driven dynamical systems.

The term flicker noise is sometimes used to refer to pink noise, although this is more properly applied only to its occurrence in electronic devices due to a direct current. Web Site for Perfectly Random Sampling with Markov Chains: There is a chapter on ``Coupling from the past,'' by James G.

Propp and David B. Wilson, Chapter 22 of the textbook ''Markov Chains and Mixing Times,'' by David A. Levin, Yuval Peres, and Elizabeth L. Lévy flight. The term "Lévy flight" was coined by Benoît Mandelbrot,[1] who used this for one specific definition of the distribution of step sizes.

He used the term Cauchy flight for the case where the distribution of step sizes is a Cauchy distribution,[2] and Rayleigh flight for when the distribution is a normal distribution[3] (which is not an example of a heavy-tailed probability distribution). Later researchers have extended the use of the term "Lévy flight" to include cases where the random walk takes place on a discrete grid rather than on a continuous space.[4][5] A Lévy flight is a random walk in which the steps are defined in terms of the step-lengths, which have a certain probability distribution, with the directions of the steps being isotropic and random.

The particular case for which Mandelbrot used the term "Lévy flight"[1] is defined by the survivor function (commonly known as the survival function) of the distribution of step-sizes, U, being[6] John Nolan's Stable Distribution Page. Applications of Heavy Tailed Distributions in Economics, Engineering and Statistics Conference. 3-5 June 1999. mathestate Web site for working on quantitative real estate problems, including some sections on stable distributions.

For learning and theoretical experimentation purposes, choose Tools -> Tutorial Tools -> Tool #4 “Risk, Variation, and Tail Behavior”. For estimating stable parameters from your own data set, choose Tools -> Hands On Tools -> Tool #7 “Stable Data Analysis”. Mathematica package for stable distributions.

Autoregressive conditional heteroskedasticity. ARCH(q) model Specification[edit] Suppose one wishes to model a time series using an ARCH process.

Let. Nakagami distribution. The Nakagami distribution or the Nakagami-m distribution is a probability distribution related to the gamma distribution.

It has two parameters: a shape parameter and a second parameter controlling spread, Characterization[edit] Credit Scoring, Data Mining, Predictive Analytics, Statistics, StatSoft Electronic Textbook. "Thank you and thank you again for providing a complete, well-structured, and easy-to-understand online resource.

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