Goodness‐of‐fit tests for the hyperbolic distribution

The authors give tests of fit for the hyperbolic distribution, based on the Cramer-von Mises statistic W2. They consider the general case with four parameters unknown, and some specific cases where one or two parameters are fixed. They give two examples using stock price data.

[1]  H. Heywood.  The Physics of Blown Sand and Desert Dunes , 1941, Nature.

[2]  Ganapati P. Patil,et al.  Statistical Distributions in Scientific Work , 1981 .

[3]  N. Fieller,et al.  Statistics of Particle Size Data , 1992 .

[4]  Ralph B. D'Agostino,et al.  Goodness-of-Fit-Techniques , 2020 .

[5]  Michael A. Stephens,et al.  Asymptotic Results for Goodness-of-Fit Statistics with Unknown Parameters , 1976 .

[6]  O. Barndorff-Nielsen.  Exponentially decreasing distributions for the logarithm of particle size , 1977, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[7]  Pedro Puig,et al.  Tests of Fit for the Laplace Distribution, With Applications , 2000, Technometrics.

[8]  E. Eberlein,et al.  Hyperbolic distributions in finance , 1995 .

[9]  W. J. McGill,et al.  Random fluctuations of response rate , 1962 .

[10]  Jens Ledet Jensen,et al.  The Fascination of Sand , 1985 .

[11]  Jens Ledet Jensen,et al.  Multivariate Distributions of Hyperbolic Type , 1981 .

[12]  P. Blæsild.  The two-dimensional hyperbolic distribution and related distributions, with an application to Johannsen's bean data , 1981 .

[13]  D. Hinkley,et al.  Estimation of the Pareto law from underreported data: A further analysis , 1977 .

[14]  O. E. Barndorff-Nielsen,et al.  Wind shear and hyperbolic distributions , 1989 .

[15]  Geoffrey S. Watson,et al.  Distribution Theory for Tests Based on the Sample Distribution Function , 1973 .

[16]  J. Imhof.  Computing the distribution of quadratic forms in normal variables , 1961 .