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 ?
The standard Cauchy distribution (Student's t-distribution with one degree of freedom) has neither a moment-generating function nor finite moments of order greater than or equal to one [Johnson et al.
Very briefly, the Cauchy distribution has unknown mean and variance, but defined median and mode.
For the heavy tailed approaches, Student's t with degrees of freedom estimated by the EM algorithm, the Cauchy distribution, and the Slash distribution with degrees of freedom estimated by the EM algorithm were all used.
For example Cauchy distribution sample TLM were unbiased to the corresponding population quantities and more robust to outliers as reported by (Elamir and Seheult, 2003).
To further explore and exploit the solution space, the uniform distribution is replaced with the other two probability distributions, and they are normal distribution [21-23] and Cauchy distribution [22, 23], respectively.
When the distribution is heavy-tailed, such as the Cauchy distribution, then ARE([bar.
2, 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.
Values of this shift are drawn from a Cauchy distribution with scale parameter [lambda] [equivalent to] [v.
Various statistics are available to test the null hypothesis of normality, but not for the Cauchy distribution, the other extreme.
For the Cauchy distribution we found a simple but very tight (p = 0.
Recently, Cauchy distribution, [22, 23] as a member of S[alpha]S (Symmetric alpha Stable) distributions, has been an alternative solution applicable to the same problem.