Hyperbolic Distribution
Hyperbolic Distribution
In this Demonstration we visualize the probability density function of the hyperbolic distribution, which has parameters (location), (tail), (asymmetry), and (scale). These are all real-valued, with the additional constraint that . 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.
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α>β