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).