Re: Low hanging fruit - Accelerated random distribution functions

[Paul Kienzle]

On Feb 22, 2007, at 7:29 PM, Paul Kienzle wrote:

> On Feb 22, 2007, at 11:46 AM, David Bateman wrote:
>
> > I haven't tried to convert the functions geornd,
>
> Octave uses the following; it would be hard to beat:
>
>    rnd(k) = floor (log (rand (size (k))) ./ log (1 - p(k)));

On second thought,

        rnd = floor(-rande(n)) ./ log(1-p)

is 2x faster.

> > wblrnd
>
> Fast enough:
>
>   rnd = scale * -log(1-rand(k))) .^ (1/shape)

1-U and U are equivalent generators, so this should be
equivalent to:

   rnd = scale * rande(size) ^ (1/shape)

which will be a bit faster.

Note that simplifying the expression on the wikipedia page
for the exponential distribution relating it to weibull
distribution gives the same result.