## Computational aspects of Cui-Freeden statistics for equidistribution on the sphere

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- by Christine Choirat and Raffaello Seri PDF
- Math. Comp.
**82**(2013), 2137-2156 Request permission

## Abstract:

In this paper, we derive the asymptotic statistical properties of a class of generalized discrepancies introduced by Cui and Freeden (SIAM J. Sci. Comput., 1997) to test equidistribution on the sphere. We show that they have highly desirable properties and encompass several statistics already proposed in the literature. In particular, it turns out that the limiting distribution is an (infinite) weighted sum of chi-squared random variables. Issues concerning the approximation of this distribution are considered in detail and explicit bounds for the approximation error are given. The statistics are then applied to assess the equidistribution of Hammersley low discrepancy sequences on the sphere and the uniformity of a dataset concerning magnetic orientations.## References

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## Additional Information

**Christine Choirat**- Affiliation: Department of Economics, School of Economics and Business Administration, Universidad de Navarra, Edificio Amigos, 31080 Pamplona, Spain
- Email: cchoirat@unav.es
**Raffaello Seri**- Affiliation: Dipartimento di Economia, Università degli Studi dell’Insubria, Via Monte Generoso 71, 21100 Varese, Italy
- MR Author ID: 710036
- Email: raffaello.seri@uninsubria.it
- Received by editor(s): October 30, 2010
- Received by editor(s) in revised form: February 9, 2012
- Published electronically: April 29, 2013
- © Copyright 2013
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp.
**82**(2013), 2137-2156 - MSC (2010): Primary 33C55, 60F05, 62E20; Secondary 86-08, 86A32, 11K45
- DOI: https://doi.org/10.1090/S0025-5718-2013-02698-1
- MathSciNet review: 3073194