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## Re: betarnd function

**From**: |
Paul Kienzle |

**Subject**: |
Re: betarnd function |

**Date**: |
Thu, 22 Feb 2007 20:50:09 -0500 |

On Feb 22, 2007, at 5:32 PM, antonio palestrini wrote:

I use the standard "inversion method" of a distrib function. That is,
function p = pareto_rnd(k,a,n)
p = k*rand(n,1).^(-1/a);
endfunction
where "k" is the location parameter and "a" the shape parameter.
The asymptotic properties of such distrib. requires n large. Even
though the above function is fast since is vectorized, do you know of
a faster octave function?

Rewriting slightly,
rnd = k * exp ( - log (rand(n)) / a )
The function rande returns values from the standard
exponential, distribution, which is -log(uniform),
so the following should work for pareto and be a bit
faster:
rnd = k * exp ( rande(n) / a)
octave> tic; 5 * exp ( - log ( rand(400) ) / 20 ); toc
ans = 0.32883
octave> tic; 5 * exp ( rande(400) / 20 ); toc
ans = 0.19606
The rande() call itself is 1/4 of this.
You could probably develop your own ziggurat code for
particular pareto parameters and see similar speed
gains, but I doubt this is worth the effort --- just
summing an array this big takes as much time as rande(),
and surely your simulation code is an order of magnitude
more complex than that.
- Paul