TITLE(Cauchy @@ The Cauchy Distribution)
USAGE(
dcauchy(x, location=0, scale=1)
pcauchy(q, location=0, scale=1)
qcauchy(p, location=0, scale=1)
rcauchy(n, location=0, scale=1)
)
ALIAS(dcauchy)
ALIAS(pcauchy)
ALIAS(qcauchy)
ALIAS(rcauchy)
VALUE(
These functions provide information about the Cauchy distribution
with location parameter LANG(location) and scale parameter LANG(scale).
PARA
LANG(dcauchy), LANG(pcauchy), and LANG(qcauchy) are respectively the density,
distribution function and quantile function of the Cauchy distribution.
LANG(rcauchy) generates random deviates from the Cauchy.
PARA
The Cauchy distribution with location EQN(l) and scale EQN(s)
has density
DEQN(f (x) = OVER(1 @@ greekpi s )
SUP(PAREN( 1 + SUP(PAREN(OVER(x-l @@ s ))@@2) ) @@ -1)
@@f(x) = 1 / (pi s (1 + ((x-l)/s)^2)))
for all EQN(x).
)
SEEALSO(
LANG(LINK(dt)) for the T distribution which generalizes 
LANG(dcauchy(*, l=0,s=1)).
)
EXAMPLES(
dcauchy(-1:4) == 1 / (pi*(1 + (-1:4)^2))
)
KEYWORD(distribution)

