A method for generating uniformly scattered points on the \(L_p\)-norm unit sphere and its applications. (English) Zbl 1433.65009
Summary: Y. Tashiro [Ann. Inst. Stat. Math. 29, 295–300 (1977; Zbl 0437.65008)] studied methods for generating unform points on the surface of the regular unit sphere. The \(L_p\)-norm unit sphere is a generalization of the regular unit sphere. In this paper, we propose a method associated with an algorithm for generating uniformly scattered points on the \(L_p\)-norm unit sphere and discuss its applications in statistical simulation, representative points of a wide class of multivariate probability distributions and optimization problems. Some examples are illustrated for these applications.
MSC:
| 65C10 | Random number generation in numerical analysis |
| 94A20 | Sampling theory in information and communication theory |
Citations:
Zbl 0437.65008References:
| [1] | Fang KT, Kotz S, Ng KW (1990) Symmetric multivariate and related distributions. Chapman and Hall, London · Zbl 0699.62048 |
| [2] | Fang KT, Wang Y (1994) Number-theoretic methods in statistics. Chapman and Hall, London · Zbl 0925.65263 |
| [3] | Goodman IR, Kotz S (1973) Multivariate {\(\beta\)}-generalized normal distributions. J Multivar Anal 3:204–219 · Zbl 0277.62040 · doi:10.1016/0047-259X(73)90023-7 |
| [4] | Gupta AK, Song D (1997) L p -norm spherical distributions. J Stat Plan Infer 60:241–260 · Zbl 0900.62270 · doi:10.1016/S0378-3758(96)00129-2 |
| [5] | Hua LG, Wang Y (1981) The application of number theory to approximate analysis. Science Press, Beijing |
| [6] | Johnson ME (1987) Multivariate statistical simulation. Wiley, New York · Zbl 0604.62056 |
| [7] | Niederreiter H (1992) Random number generation and quasi-Monte Carlo methods. SIAM, Philadelphia · Zbl 0761.65002 |
| [8] | Rosenblatt M (1952) Remarks on a multivariate transformation. Ann Math Stat 23:470–472 · Zbl 0047.13104 · doi:10.1214/aoms/1177729394 |
| [9] | Sloan IH, Joe S (1994) Lattice methods for multiple integration. Oxford University Press, Oxford · Zbl 0855.65013 |
| [10] | Song D, Gupta AK (1997) L p -norm uniform distribution. Proc Am Math Soc 125(2):595–601 · Zbl 0866.62026 · doi:10.1090/S0002-9939-97-03900-2 |
| [11] | Tashiro D (1977) On methods for generating uniform points on the surface of a sphere. Ann Inst Stat Math 29:295–300 · Zbl 0437.65008 · doi:10.1007/BF02532791 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
