Cauchy distribution

The Cauchy-Lorentz distribution, named after Augustin Cauchy, is a continuous probability distribution with probability density function

Related Topics:
Augustin Cauchy - Probability distribution - Probability density function

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: f(x; x_0,gamma) = rac{1}{pigamma left} !

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where x0 is the location parameter, specifying the location of the peak of the distribution, and γ is the scale parameter which specifies the half-width at half-maximum (HWHM). As a probability distribution, it is known as the Cauchy distribution while among physicists it is known as the Lorentz distribution or the Breit-Wigner distribution. Its importance in physics is largely due to the fact that it is the solution to the differential equation describing forced resonance. In spectroscopy it is the description of the line shape of spectral lines which are broadened by many mechanisms including resonance broadening. The statistical term Cauchy distribution will be used in the following discussion.

Related Topics:
Location parameter - Scale parameter - Physics - Differential equation - Resonance - Spectroscopy

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The special case when x0 = 0 and γ = 1 is called the standard Cauchy distribution with the probability density function

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: f(x; 0,1) = rac{1}{pi (1 + x^2)}. !

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