Hyperbolic Distribution

location parameter μ

0

tail parameter α

1

asymmetry parameter β

0

scale parameter δ

1

log scale

In this Demonstration we visualize the probability density function of the hyperbolic distribution, which has parameters

μ

(location),

α

(tail),

β

(asymmetry), and

δ

(scale). These are all real-valued, with the additional constraint that

α>β

. This distribution has "semi-heavy" tails and has appeared in a diverse range of applications, including models of asset returns in financial markets and sand pile formation. The word "hyperbolic" is used because the log of its probability density function is a hyperbola; this can be seen by clicking the "log scale" checkbox.