Cauchy
The Cauchy Distribution
Description
Calculates density, cumulative probability, quantile, and
generate random sample for the Cauchy distribution (continuous).
Usage
dcauchy(x, location = 0, scale = 1, log = FALSE) # density
pcauchy(q, location = 0, scale = 1, lower.tail = TRUE, log.p = FALSE) # probability
qcauchy(p, location = 0, scale = 1, lower.tail = TRUE, log.p = FALSE) # quantile
rcauchy(n, location = 0, scale = 1) # random
Arguments
| x, q |
numeric vectors in the range (-Inf, Inf) that specify the quantiles.
|
| p |
a numeric vector in the range [0, 1] that specifies the probabilities.
|
| n |
an integer scalar in the range [0, Inf) that specifies the number of random samples requested.
If the input value is not an integer, it is truncated.
If length(n) is greater than 1,
the random function returns length(n) random samples.
|
| location |
a numeric vector in the range (-Inf, Inf) that specifies the location parameter.
|
| scale |
a numeric vector in the range [0, Inf) that specifies the scale parameter.
|
| log |
a logical value.
If FALSE (default), the density function returns the density itself.
If TRUE, it returns the log of the density.
|
| lower.tail |
a logical value.
If TRUE (default), the probability supplied to the quantile function
or returned by the probability function is P[X <= x].
If FALSE, it is P[X > x].
|
| log.p |
a logical value.
If FALSE (default), the probability supplied to the quantile function
or returned by the probability function is the probability itself.
If TRUE, it is the log of the probability.
|
Details
The distribution parameter(s) are replicated cyclically to be the same length as
the input x, q, p, or the number of random samples requested.
Missing values (NAs) in the input or the distribution parameter(s)
will cause the corresponding elements of the result to be missing.
Value
returns density (dcauchy),
cumulative probability (pcauchy),
quantile (qcauchy), or
random sample (rcauchy)
for the Cauchy distribution with parameters location and scale.
Side Effects
If the .Random.seed dataset exists, the random sample function updates its value.
The random sample function creates the .Random.seed dataset if it does not exist.
Background
The Cauchy distribution is a family of continuous probability distributions
defined on the interval (-Inf, Inf) and parameterized by location, which specifies the location of the peak of the distribution, and scale, which specifies the half-width at half-maximum.
References
Johnson, N. L. and Kotz, S. (1970).
Continuous Univariate Distributions, vol. 1.
Houghton-Mifflin, Boston.
See Also
Examples
rcauchy(20,0,10) #sample of 20, location 0, scale 10