.BG
.FN Cauchy
.FN dcauchy
.FN pcauchy
.FN qcauchy
.FN rcauchy
.TL
Cauchy Distribution
.CS
dcauchy(q, location=0, scale=1)
pcauchy(q, location=0, scale=1)
qcauchy(p, location=0, scale=1)
rcauchy(n, location=0, scale=1)
.AG q
vector of quantiles.
Missing values (`NA's) are allowed.
.AG p
vector of probabilities.
Missing values (`NA's) are allowed.
.AG n
sample size.
If `length(n)' is larger than 1, then `length(n)' random values are returned.
.AG location
vector of location parameters.
.AG scale
vector of (positive) scale parameters.
.RT
density (`dcauchy'),
probability (`pcauchy'),
quantile (`qcauchy'), or
random sample (`rcauchy')
for the cauchy distribution with parameters `location' and `scale'.
.SP
.Tr
The density function is given by
.sp
.EQ
delim $$
f sub l,s ( q ) ~=~
1 over { pi s ( 1 ~+~ ( q - l ) / s ) sup 2 } , ~~~ s ~>~ 0,
.EN
.sp
where $l$ and $s$ are the `location' and `scale' parameters.
.En
.SE
The function `rcauchy' causes creation of the dataset `.Random.seed' if it does
not already exist, otherwise its value is updated.
.EX
rcauchy(20,0,10) #sample of 20, location 0, scale 10
.KW distribution
.EQ
delim off
.EN
.WR
