Posted by C. (http://symcbean.blogspot.com/) on 02/01/08 13:31

On 31 Jan, 19:29, The Natural Philosopher <a...@b.c> wrote:
> Fred wrote:
> > Hi guys,
>
> > I was wondering how could i get a random number exemple between 1 and
> > 100 but with n% of getting some value over a number x.
>
> > Thanks a lot in advance.
>
> > Fred
>
> Never mind Jerry, No one else does.
>
> So you want a random number from a weighted distribution?
>
> Your spec doesn't contain quite enough data to formulate the formula,
> since there are an infinite number of distributions that have N% over
> value X..
>
> One example, is that you first of all get a random number between 0 and
> 100: If this is greater than N, then select a random number greater than
> X, else select one less than X.
>
> So in pseudo code where RAND(X) returns a number between 0 and X-1...
>
> if ((RAND(100))<N) THEN RETURN RAND(X) ELSE RETURN(X+RAND(100-X));

This is not a god way to get a weighted distribution (and the OP is
NOT asking for a weighted distribution) - you should just generate one
floating point number and apply a transformation function to it.
Continuous transformations are quite difficult but since for a
possible range of 100 integer values a discontinuous transformation
would be adequate - something like:

function transform($in)
{
if (($in<0) || ($in>100)) trigger_error('out of range');
$mul=array(
1=>10, 5=>9, 10=>7, 15=>6....40=>1, 50=>0.9, 55=>0.8...
);
return($in * $mul[5*(integer)($in/20)]);
}

Note the values above will emphasize the mean rather than what the OP
was asking for, but could be adapted for purpose by tweaking the $mul
values.

C.

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