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In article 15051@head-cfa.harvard.edu, dj@head-cfa.harvard.edu (Diab Jerius) writes:
>i have come across references to a non-central chi-squared distribution
>in the statlib/netlib random number generator package ranlib.
>it is described in the accompanying documentation as being the sum of a
>chi-squared deviate with df-1 degrees of freedom and the square of a normal
>deviate with standard deviation of 1 and non-zero mean.
>
>i am totally ignorant as to what these distributions are based on or what
>they're use might be, but from the name of the beast i may have some
>use for it.  
>
>i have searched through quite a few probability and statistics references,
>but none seems to describe this distribution.  can anyone point me to
>a reference or perhaps briefly describe from whence it arose and what
>its use might be?
>
>
>thanks much!
>
>diab
>-- 
>------------------------------------------------------------------------------
>diab jerius                     | harvard-smithsonian center for astrophysics   
>jerius@cfa.harvard.edu          | 60 garden st., m/s 81,  cambridge ma  02138  
>                                | vox: 617-496-7575         fax: 617-495-7356




These are generated, for example, by mean-reverting square root processes, ie:

Let X be a positive stochastic variable, K and u be parameters. Then the
stochastic differential equation


	dX = K( u - X ) dt + sqrt(X) dz

where dz is a brownian process, will generate a non-central Chi2 distribution
for X as a function of time t. 


Usual disclaimers,

	PB.