A method for approximate inversion of the hyperbolic CDF. (English) Zbl 1239.65008

Summary: It has been observed by E. Eberlein and U. Keller [Bernoulli, 1, 281–299 (1995; Zbl 0836.62107)] that the hyperbolic distribution fits logarithmic rates of returns of a stock much better than the normal distribution. We give a method for sampling from the hyperbolic distribution by the inversion method, which is suited for simulation using low discrepancy point sets. Instead of directly inverting the cumulative distribution function (CDF) we provide an approximation of the inverse function which is simple to obtain by standard numerical methods and which is fast to compute.


65C50 Other computational problems in probability (MSC2010)
62D05 Sampling theory, sample surveys
62E10 Characterization and structure theory of statistical distributions
65R10 Numerical methods for integral transforms
91G80 Financial applications of other theories


Zbl 0836.62107
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