Density, distribution function, quantile function and random
generation for the Cauchy distribution with location parameter
location and scale parameter
1 2 3 4
vector of quantiles.
vector of probabilities.
number of observations. If
location and scale parameters.
logical; if TRUE, probabilities p are given as log(p).
logical; if TRUE (default), probabilities are P[X ≤ x], otherwise, P[X > x].
scale are not specified, they assume
the default values of
The Cauchy distribution with location l and scale s has density
f(x) = 1 / (π s (1 + ((x-l)/s)^2))
for all x.
qcauchy are respectively
the density, distribution function and quantile function of the Cauchy
rcauchy generates random deviates from the
The length of the result is determined by
rcauchy, 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.
qcauchy are all calculated
from numerically stable versions of the definitions.
rcauchy uses inversion.
Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, volume 1, chapter 16. Wiley, New York.
Distributions for other standard distributions, including
dt for the t distribution which generalizes
dcauchy(*, l = 0, s = 1).
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