Re: Fwd: [Help-gsl] random number distributions

[John D Lamb]

John Gehman wrote:
> if you like  check out R.W. Hamming "Numerical Methods for Scientists 
> and  Engineers", -- you can generate a gaussian random number by 
> summing 12  uniform random numbers and subtract 6.0. There's a subtle 
> caveat which  explains that this isn't perfect, but in most cases is 
> actually closer  to what you want than a perfectly gaussian random 
> number (i.e. do you  ever really want random number which has 
> probability of 137*sigma, even  if strictly speaking it's bound to 
> happen sooner or later in a true  gaussian distribution?)
>
> Begin forwarded message:
>
> > I wish to use _in same program_ a random number generator which  
> > provides uniformly distributed random numbers _and_ a function which  
> > returns a Gaussian random variate.
> > Theses functions requires two calls to a random number generator.
> > So, I'm wondering whether I have to set one or two random number  
> > generator ?
> > Thanks in advance,
> > Regards,
There is nothing to stop you using two random number generators, though 
you probably only need one. If you use two random number generators with 
the same seed and call them equally often then the results will be 
strongly correlated. If you use just one they will be nearly 
uncorrelated. So I use one unless there's a good reason to do otherwise.

gsl_ran_gaussian is more accurate and often faster than summing random 
numbers because it uses an exact method. Speed will depend on the speed 
of the random number generators, whcih depends on the quality. Typically 
the better quality random number generators are slower. gsl_ran_gaussian 
uses (I think) Box-Müller, which requires on average one call to the 
random number generator per gaussian variate. The ziggurat method (on 
the GSL web pages), maybe in the latest gsl release is faster than 
Box-Müller for any gsl random number generator.