dcauchy(x, location=0, scale=1, log=F) pcauchy(q, location=0, scale=1) qcauchy(p, location=0, scale=1) rcauchy(n, location=0, scale=1, bigdata=F)
bdVector
of quantiles.
Missing values (
NA
s) are allowed.
bdVector
of quantiles.
Missing values (
NA
s) are allowed.
bdVector
of probabilities.
Missing values (
NA
s) are allowed.
length(n)
is larger than 1, then
length(n)
random values are returned.
bdVector
of location parameters.
This is replicated to be the same length as
p
or
q
or the number of
deviates generated.
Missing values are not accepted.
bdVector
of (positive) scale parameters.
This is replicated to be the same length as
p
or
q
or the number of
deviates generated.
Missing values are not accepted.
TRUE
, an object of type
bdVector
is returned.
Otherwise, a
vector
object is returned. This argument can be used only if the bigdata library section has been loaded.
TRUE
,
dcauchy
will return
the log of the density, not the density itself.
dcauchy
),
probability (
pcauchy
),
quantile (
qcauchy
), or
random sample (
rcauchy
)
for the cauchy distribution with parameters
location
and
scale
.
rcauchy
causes creation of the dataset
.Random.seed
if it does
not already exist, otherwise its value is updated.
Elements of
q
or
p
that are missing will cause the corresponding elements of the result to be missing.
The Cauchy is a real valued distribution symmetric about
location
, and
has long enough tails that the expectation does not exist.
The default distribution is the same as Student's t distribution with
one degree of freedom (see
T
).
The harmonic mean of variates that have positive density at 0 is typically
distributed as Cauchy. The Cauchy also appears in the theory of Brownian
motion.
For details on the uniform random number generator implemented in S-PLUS,
see the
set.seed
help file.
Johnson, N. L. and Kotz, S. (1970). Continuous Univariate Distributions, vol. 1. Houghton-Mifflin, Boston.
rcauchy(20,0,10) #sample of 20, location 0, scale 10