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Cauchy-Lorentz Distribution

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on

Jul 24, 2020, 6:28:07 PM

Created by

on

Aug 10, 2016, 4:05:30 PM

f_{x} = \frac{1}{π \cdot γ [1 + {(\frac{x - x_{0}}{γ})}^{2}]}

$f_x = 1/(pi*gamma[1+((x-x_0)/gamma)^2]$

(γ) scale parameter

$(gamma)"scale parameter"$

(x) variable

$(x)"variable"$

(x_{0}) location parameter

$(x_0)"location parameter"$

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428304cb-5f14-11e6-9770-bc764e2038f2

The Cauchy-Lorentz Distribution is a continuous probability distribution. It is the distribution of the X-intercept of a ray issuing from ( $x_{0}, γ$ $x_0, gamma$ ) with a uniformly distributed angle. Its importance in physics is the result of it being the solution to the differential equation describing forced resonance.
The following formula is used: $f_{x} = \frac{1}{π \cdot γ [1 + {(\frac{x - x_{0}}{γ})}^{2}]}$ $f_x=1/(pi*gamma[1+((x-x_0)/gamma)^2]$ , where:

$γ$ $gamma$ = scale parameter
$x$ $x$ = variable
$x_{0}$ $x_0$ = location parameter

References

Wikipedia (https://en.wikipedia.org/wiki/Cauchy_distribution)

This equation, Cauchy-Lorentz Distribution, references 1 page

Equations and Data Items

•

π

$pi$ by MichaelBartmess

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