http://imagej.273.s1.nabble.com/Gaussian-Random-Number-Generation-tp5021203p5021207.html
Mark’s suggestion is the Box and Muller algorithm: Box G, Muller M. A Note on the Generation of Random Normal Deviates. Ann Math Stat. 1958;29:610-611. It works well, but I’ve found that with many random number generators X and Y tend to be correlated. You can check this by plotting X vs Y for a few hundred calculations. If there is a recognizable pattern (stripes, clusters) on the plot, X and Y are correlated (and thus not random). I generally use only one of the pair if I really need a set of pseudorandom numbers that look truly random.
> On Sep 19, 2018, at 9:09 AM, Mark Osborne <
[hidden email]> wrote:
>
> Greg
>
> Something like the following macro should work...
>
> var U; var V;
>
> function normal(){
> S = 2;
> while(S >= 1){
> U = -1+2*random; // uniform random no. -1..1
> V = -1+2*random;
> S = U*U+V*V;
> }
> }
>
> X = U * sqrt(-2*log(S)/S); //or
> Y = V * sqrt(-2*log(S)/S); // where log in ImageJ is natural ln
>
> X and Y are independent standard normally distributed random numbers, so you can multiply by a finite standard deviation to spread beyond unit STD and add to a mean to get the Gaussian. Check against the Marsaglia polar method of generating normally distributed random numbers. Bit wasteful finding S<1, but easy to check and rather more intuitive than some.
>
> Mark
>
> -----Original Message-----
> From: ImageJ Interest Group [mailto:
[hidden email]] On Behalf Of Seitz Arne
> Sent: 19 September 2018 13:33
> To:
[hidden email]
> Subject: Re: Gaussian Random Number Generation
>
> Dear Greg,
>
> the RandomJ plugin from Eric Meijering looks to me what you are asking for.
>
https://imagescience.org/meijering/software/randomj/>
> The only limitation it works on images. However it is macro recordable and the source code can be found on GitHub.
>
> Best
> Arne
>
>
> -----Original Message-----
> From: ImageJ Interest Group [mailto:
[hidden email]] On Behalf Of JAMES, gregory (SANDWELL AND WEST BIRMINGHAM HOSPITALS NHS TRUST)
> Sent: mercredi 19 septembre 2018 14:09
> To:
[hidden email]
> Subject: Gaussian Random Number Generation
>
> Dear ImageJ community,
>
>
> You are an intelligent group of people so I would like to ask this...
>
>
> Does anyone have a clever way of generating a random set of numbers that conform to a normal (Gaussian) distribution for a given mean and standard deviation using the 'random' macro function? I acknowledge that the ImageJ macro language is a slightly strange place to do this but I cannot use Excel because my data sets are so large and I would rather not learn a new scripting language (e.g. R).
>
>
> For what it's worth, it is quite straightforward to do in Excel using =NORMINV(RAND(), mean, stdev). Does anyone have a clever way of replicating this function in ImageJ?
>
>
> Many thanks,
>
>
> Greg.
>
>
> __________________________________________
> Gregory James
> Clinical Scientist (Nuclear Medicine)
> Department of Physics and Nuclear Medicine City Hospital Dudley Road Birmingham
> B18 7QH
>
> 0121 507 4043
>
>
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