Cauchy distribution
The Cauchy distribution is a probability distribution with probability density function:
- <math> f(x) = \frac{1}{s*\pi*[1 + ((x-t)/s)^2]} </math>
where t is the location parameter and s is the scale parameter. The special case when t = 0 and s = 1 is called the standard Cauchy distribution with the probability density function:
- <math> f(x) = \frac{1}{\pi (1 + x^2)} </math>
The Cauchy distribution is often cited as an example of a distribution which has no mean, variance or higher moments defined, although its mode and median are well defined and both zero.
When U and V are two independent normal random variables with standard normal distributions, then the ratio U/V has the standard Cauchy distribution.
The Cauchy distribution is sometimes called the Lorentz distribution
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living-room; Raphael-eyed little imps, going sidewise on their
to give a religious air, and a great sheaf of wild bloom
schoolhouse, with the fine-drawn altar cloths, the beaten silver
up mule-back from Old Mexico forty years ago. All in white the
body of their Lord, and Tomaso, who is priest's boy, tries not to
and a bottle of wine that ripened on the sunny slope of Escondito.
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accommodate the large laugh that lives in him, but a most shrewd
his confessional, and I for my part believe it.
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each a new dress apiece, the senoras a new rebosa. The
unspeakable ties, silk handkerchiefs, and new leathers to their
young quail cry "cuidado," "have a care!" you can hear the
comfortable old dames, whose experience gives them the touch of art,
to have school begin on the first of September, but got nothing
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streets, "Vive la Libertad!" answered from the houses and
shots are fired commemorating the tragedy of unhappy Maximilian,
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Montezuma before it touches the vineyards and the town, and the day
the Declaration of Independence and an address punctured by
horsemanship that make lathered bits and bloody spurs; also a
play the flute, a little lean man with a saintly countenance, young
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