Cauchy Distribution

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Cauchy distribution [kō·shē dis·trə′byü·shən]

(statistics)

A distribution function having the formM/[πM²+ (x-a)²], wherexis the variable andMandaare 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.

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No references found			Values of this shift are drawn from a Cauchy distribution with scale parameter [lambda] [equivalent to] [v. Bounds on time reversal violation from polarized neutron capture with ... by Sharapov, E.I. / Journal of Research of the National Institute of Standards and Technology 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. Understanding statistics using computer demonstrations by Dunn, Peter K. / Journal of Computers in Mathematics and Science Teaching 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. Understanding statistics using computer demonstrations by Dunn, Peter K. / Journal of Computers in Mathematics and Science Teaching			Caucasian Brown Cattle Caucasian Bureau of the Central Committee of the Rcp Bolshevik Caucasian Cattle Caucasian Committee Caucasian Fine-Wooled Sheep Caucasian Gates Caucasian Languages Caucasian Line Cossack Host Caucasian Mineral Waters Region Caucasian Preserve Caucasian Race Caucasian Regional Committee of the Rcp Bolshevik Caucasian Union Committee of the Rsdlp Caucasian War of 1817–64 Caucasoid Caucasus Caucasus Indicus Caucasus Mountains Cauchon, Bishop Cauchon, Pierre Cauchy Cauchy boundary conditions Cauchy condensation test Cauchy data Cauchy dispersion formula Cauchy Distribution Cauchy formula Cauchy frequency distribution Cauchy horizon Cauchy inequality Cauchy Integral Cauchy integral formula Cauchy integral test Cauchy integral theorem Cauchy mean Cauchy mean-value theorem Cauchy net Cauchy number Cauchy principal value Cauchy Problem Cauchy product Cauchy radical test Cauchy random variable Cauchy ratio test Cauchy relations Cauchy residue theorem Cauchy sequence Cauchy surface Cauchy Theorem Cauchy transcendental equation Cauchy's Inequality			Caucasus Mountains Caucasus Range Caucasus Range Caucasus Region Caucasus Region Caucasus Research Resource Center Caucasus School of Journalism and Media Management Caucasus Youth Environmental Network Caucausian Caucausian Caucausian CAUCE Caucho Caucho Caucho Cauchon, Bishop Cauchon, Pierre Cauchy Cauchy Cauchy boundary condition Cauchy boundary conditions Cauchy complete Cauchy complete space Cauchy completeness Cauchy completion Cauchy condensation test Cauchy criteria for uniform convergence Cauchy criterion for uniform convergence Cauchy data Cauchy dispersion formula Cauchy Distribution Cauchy formula Cauchy frequency distribution Cauchy horizon Cauchy inequality Cauchy integral Cauchy integral formula Cauchy integral test Cauchy integral theorem Cauchy integral theorem Cauchy mean Cauchy mean theorem Cauchy mean-value theorem Cauchy multiplication Cauchy net Cauchy noise Cauchy number Cauchy principal part Cauchy principal part integral Cauchy principal value Cauchy problem Cauchy problems Cauchy product Cauchy radical test Cauchy Random Variable Cauchy ratio test

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