Cauchy distribution facts for kids
In mathematics, the CauchyLorentz distribution (after AugustinLouis Cauchy and Hendrik Lorentz) is a continuous probability distribution with two parameters: a location parameter and a scale parameter. As a probability distribution, it is usually called a Cauchy distribution. Physicists know it as a Lorentz distribution.
When the location parameter is 0 and the scale parameter is 1, the probability density function of the Cauchy distribution reduces to . This is called the standard Cauchy distribution.
The Cauchy distribution is used in spectroscopy to describe the spectral lines found there, and to describe resonance. It is also often used in statistics as the canonical example of a "pathological" distribution, since both its mean and its variance are undefined. The look of a Cauchy distribution is similar to that of a normal distribution, though with longer "tails".
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Estimating the mean and standard deviation through samples from a Cauchy distribution (bottom) does not converge with more samples, as in the normal distribution (top). There can be arbitrarily large jumps in the estimates, as seen in the graphs on the bottom. (Click to expand)