If scale
is omitted, it assumes the default value of 1
. The Hyperbolic distribution with parameters shape
$=\alpha$
and scale
$=\sigma$ has density proportional to
$$f(x) \sim \exp(-\alpha \sqrt{1+(\frac{x}{s})^2})$$
for all $x$, $\alpha > 0$ and $\sigma > 0$.
The generation algorithm uses transformed density rejection TDR. The
parameters lb
and ub
can be used to generate variates from
the Hyperbolic distribution truncated to the interval (lb
,ub
).