| gensphere-package {gensphere} | R Documentation |
gensphere
Description
Define and compute with generalized spherical distributions - multivariate probability laws that are specified by a star shaped contour (directional behavior) and a radial component.
Details
This package implements some classes of generalized spherical distributions in dimensions 2, 3, and above.
Functions cfunc.new, cfunc.add.term, cfunc.finish give a flexible way to define a range of shapes for the
star-shaped contours. Then function gensphere defines a generalized spherical distribution
using a contour function and a specification of the radial term. Function dgensphere is used
to compute the multivariate density g(x) for X and function rgensphere is
used to simulate a sample random vectors with the (approximate) distribution X.
A large class of distribution can be described as generalized spherical laws.
In particular, all isotropic/radially symmetric distributions and all elliptically contoured
distributions are generalized spherical laws. Such distributions can be represented as:
\mathbf{X} = R \mathbf{S}
where R is a positive random variable and S is a random vector distributed uniformly (with respect to surface area) on
the contour, see Nolan (2015).
Throughout this package, points in d-dimensional space are represented as column vectors; this is different than what base R and packages mvmesh, geometry, etc. use; but it is the same as package SphericalCubature, SimplicialCubature, and other packages.
This research was supported by an agreement with Cornell University, Operations Research & Information Engineering, under contract W911NF-12-1-0385 from the Army Research Development and Engineering Command.
Please let me know if you find any mistakes. I will try to fix bugs promptly. Constructive comments for improvements are welcome; actually implementing any suggestions will be dependent on time constraints.
Version 1.0 was released on 18 May 2016. Version 1.1 was released on 13 September 2017 and includes a new optional argument norm.const.method in the function cfunc.finish. Also changes were made to accomodate changes in package SphericalCubature.
Version 1.2 (never on CRAN, 10 January 2021) has a minor change to work with the update of package
SphericalCubature to version 1.5, updated a reference, and the
examples include if( interactive() ) around calls to plotting functions.
Version 1.3 (12 January 2021) adds links to the DOI for the paper this work
is based on, and provides a faster 3-d example.
Author(s)
John P Nolan
Maintainer: John P Nolan
References
B. C. Arnold, E. Castillo and J. M. Sarabia (2008), Multivariate distributions defined in terms of contours, J. Stat. Planning and Inference, 138, 4158 - 4171
C. Fernandez, J. Osiewalksi and M. F. J. Steel (1995), Modeling and Inference with v-Spherical Distributions, J. Amer. Stat. Assoc., 90, 1331-1340
J. P. Nolan (2016), An R package for modeling and simulating generalized spherical and related distributions, J. of Statistical Distributions and Applications, 3:14, online at doi: 10.1186/s40488-016-0053-0