Encyclopedia > Cauchy distribution

  Article Content

Cauchy distribution

The Cauchy distribution is a probability distribution with probability density function:

<math> f(x) = \frac{1}{s*\pi*[1 + ((x-t)/s)^2]} </math>

where t is the location parameter and s is the scale parameter. The special case when t = 0 and s = 1 is called the standard Cauchy distribution with the probability density function:

<math> f(x) = \frac{1}{\pi (1 + x^2)} </math>

The Cauchy distribution is often cited as an example of a distribution which has no mean, variance or higher moments defined, although its mode and median are well defined and both zero.

When U and V are two independent normal random variables with standard normal distributions, then the ratio U/V has the standard Cauchy distribution.

The Cauchy distribution is sometimes called the Lorentz distribution



All Wikipedia text is available under the terms of the GNU Free Documentation License

 
  Search Encyclopedia

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
Grand Prix

... dumped 2003-03-17 with ...

 
 
 
This page was created in 22.8 ms