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- One can derive the
distribution for k degrees of
freedom in two ways.
- 1.) Mathews and Walker
- Direct calculation as for k=1 noting that
with 
of mean 0, Standard
Deviation 1 is 
where r is radial distance in k-dimensional
space.
- Then factors multiplying
in Equation (34) are just volume element in k dimensions.
- 2.) Eadie, et al. show characteristic function of
with one
degree of freedom is
- Therefore, characteristic function for
with k degrees
of freedom is 
- and this can be inverse fourier transformed to give Equation (34).
Geoffrey Fox, Northeast Parallel Architectures Center at Syracuse University, gcf@npac.syr.edu