Thanks for the enlightenment, George.
I misinterpreted what was said in Numerical Recipes, where it starts
by
referring to the Box-Muller method, then gives your algorithm without
any
intermediate referral. Hence I had always thought of this method as
being B-M.
Hey, I learnt something new, can I go home now?
;-)
Regards
Ian
"George Marsaglia" <[EMAIL PROTECTED]> wrote in message
t8Mc8.49030$[EMAIL PROTECTED]">news:t8Mc8.49030$[EMAIL PROTECTED]...
>
> Ian Buckner <[EMAIL PROTECTED]> wrote in message
> [EMAIL PROTECTED]">news:[EMAIL PROTECTED]...
> > The Box-Muller algorithm rejects roughly 22.5% of the
> > generated points. I'm not aware of any bound on the number
> > of consecutive rejections, other than a statistical one, hence
> > my statement. I would welcome correction if this is not the case.
> >
> > Regards
> > Ian
> >
> > "Radford Neal" <[EMAIL PROTECTED]> wrote in message
> > [EMAIL PROTECTED]">news:[EMAIL PROTECTED]...
> > > >Box-Muller does not work for real time requirements.
> > >
> > > This isn't true, of course. A "real time" application is one
where
> > > one must guarantee that an operation takes no more than some
> > specified
> > > maximum time. The Box-Muller method for generating normal
random
> > > variates does not involve any operations that could take
arbitrary
> > > amounts of time, and so is suitable for real-time applications.
> > >
> > > This assumes that the time needed for Box-Muller is small
enough,
> > > which will surely often be true. If the time allowed is very
small,
> > > then of course one might need to use some other method.
> > >
> > > Rejection sampling methods would not be suitable for real-time
> > > applications, since there is no bound on how many points may be
> > > rejected before one is accepted, and hence no bound on the time
> > > required to generate a random normal variate.
> > >
> > > Radford Neal
> =========================
>
> What is usually called the Box-Muller method is
> the transformation of normal variates to polar coordinates
> that we all owe to Laplace for showing us how to evaluate
> \int_0^\infty e^{-x^2}. To get a pair of independent
> standard normal variates x,y, use two [0,1) uniform variates
> U1,U2 and put
> x = sqrt(-2*ln(U1))*cos(2pi*U2)
> y = sqrt(-2*ln(U1))*sin(2pi*U2).
>
> This is a fixed-time procedure.
>
> The random-time procedure, often mistakenly
> called Box-Muller, was developed in 1956
> by Marsaglia:
>
> Generate uniform (-1,1) variates V1,V2 until
> S = V1^2 + V2^2 <1
> then return
> x = V1*sqrt(-2ln(S)/S)
> y = V2*sqrt(-2ln(S)/S).
>
> George Marsaglia
>
>
>
>
>
>
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