R: The Cauchy Distribution (original) (raw)
| Cauchy {stats} | R Documentation |
|---|
Description
Density, distribution function, quantile function and random generation for the Cauchy distribution with location parameterlocation and scale parameter scale.
Usage
dcauchy(x, location = 0, scale = 1, log = FALSE)
pcauchy(q, location = 0, scale = 1, lower.tail = TRUE, log.p = FALSE)
qcauchy(p, location = 0, scale = 1, lower.tail = TRUE, log.p = FALSE)
rcauchy(n, location = 0, scale = 1)
Arguments
| x, q | vector of quantiles. |
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| p | vector of probabilities. |
| n | number of observations. If length(n) > 1, the length is taken to be the number required. |
| location, scale | location and scale parameters. |
| log, log.p | logical; if TRUE, probabilities/densities are given as logarithms. |
| lower.tail | logical; if TRUE (default), probabilities areP[X \le x], otherwise, P[X > x]. |
Details
If location or scale are not specified, they assume the default values of 0 and 1 respectively.
The Cauchy distribution with location l and scale s has density
f(x) = \frac{1}{\pi s} \left( 1 + \left(\frac{x - l}{s}\right)^2 \right)^{-1}%
for all x.
Value
dcauchy gives the density,pcauchy is the cumulative distribution function, andqcauchy is the quantile function of the Cauchy distribution.rcauchy generates random deviates.
The length of the result is determined by n forrcauchy, and is the maximum of the lengths of the numerical arguments for the other functions.
The numerical arguments other than n are recycled to the length of the result. Only the first elements of the logical arguments are used.
Source
dcauchy, pcauchy and qcauchy are all calculated from numerically stable versions of the definitions.
rcauchy uses inversion.
References
Becker R. A., Chambers J. M., Wilks A. R. (1988).The New S Language. Chapman and Hall/CRC, London.
Johnson N. L., Kotz S., Balakrishnan N. (1994).Continuous Univariate Distributions, volume 1. Wiley, New York. ISBN 978-0-471-58495-7. Chapter 16.
See Also
Distributions for other standard distributions, including[dt](../../stats/help/dt.html) for the t distribution which generalizesdcauchy(*, l = 0, s = 1).
Examples
dcauchy(-1:4)
[Package _stats_ version 4.6.0 Index]