Cauchy Distribution


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Cauchy distribution

[kō·shē dis·trə′byü·shən]
(statistics)
A distribution function having the form M /[π M 2+ (x-a)2], where x is the variable and M and a are constants. Also known as Cauchy frequency distribution.

Cauchy Distribution

 

a special type of probability distribution of random variables. Introduced by Cauchy, it is marked by the density

The characteristic function is

f(t) = exp (μit − λ ǀ t ǀ)

The Cauchy distribution is unimodal and symmetric with respect to the point x = μ, which is its mode and median. No

Figure 1. Cauchy distribution: (a) probability density, (b) distribution function

moments of positive order of a Cauchy distribution exist. Figure 1 depicts a Cauchy distribution for μ = 1.5 and λ = 1.

References in periodicals archive ?
1, Cauchy distribution has the longest flat tails and Gaussian distribution has the shortest flat tails.
ABSTRACT: The motivation of this work is based on the observation that Cauchy distribution provides more accurate estimates of rate and distortion characteristics of video sequences than the previously used distribution such as Laplacian distribution.
Keywords: Cauchy distribution, low delay, rate control, Lagrange multiplier technique, linear regression analysis
In this connection, our work is based on the assumption that AC coefficients follow a Cauchy distribution.
Assume that, the DCT-coefficients of the motion compensated difference frame are Cauchy distribution with Cauchy parameter, m.
Cauchy distribution is the case with [alpha] = 1, [beta] = 0, [gamma], [member of] (0, + [infinity]), and [member of] (-[infinity], + [infinity]).
Values of this shift are drawn from a Cauchy distribution with scale parameter [lambda] [equivalent to] [v.
the double exponential distribution and the Cauchy distribution to
Jennrich (1995) also then provides numerous normal probability plots for random numbers from the double exponential distribution and the Cauchy distribution to indicate some typical data features that can be detected by such plots.
In some cases, such as the Laplace or Cauchy distributions, the mean is difficult or impossible to compute.