Gaussian with random numbers

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1

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Hello,

Is there a way to implement random Skewed Gaussian as it is done for normal Gaussian:

gRandom->Gaus(mean,sigma)

Something like gRandom->SkewedGaus(mean,sigma,skewness)

so that the event by event data can fill the respective tree branch.

{Not using an already user defined “SkewedGauss” and then fill the histogram randomly, like the following:
h1->FillRandom(“SkewedGauss”,number); }

Thanks.

2

Hi @moneta

Any help on this?

3

Hi Sandy,

Thanks for the post.
You can use the TF1::GetRandom method ROOT: TF1 Class Reference for this purpose, where the TF1 instance is a skewed Gaussian.

I hope this helps!

Cheers,
Danilo

4

Hi @Danilo

Thanks for your reply

Like this?

TF1 *f1 = TF1(“f1”,“function”,0,10);

h = f1->GetRandom();

5

Yes like that, as the linked documentation prescribes.

Cheers,
D

6

Hi @Danilo

Thanks.

When I do the following:

TF1 *f1 = new TF1("f1","(2.0/[1])*(TMath::Gaus(((x - [0]) / [1]), 0.0, 1.0))*(0.5 * (1.0 + erf(([2]*((x - [0]) / [1]))/1.41421356)))",0.0,1000.0,3);
f1->FixParameter(0,100.0);     // Mean             
f1->FixParameter(1,7.1);     // Sigma 
f1->FixParameter(2,2.0);    // Skewness
treevar1 = f1->GetRandom();

where, treevar1 is a variable in tree structure.
It does not complain but the program does not stop as well…
What is the mistake there? In ‘Gaus’?

7

Hi,

If you mean that the random generation takes a lot of time, it is possible. ROOT cannot optimize the generation of random numbers for every possible distribution. You can think about simplifying your distribution or think to a customised random generation if the performance achieved is not sufficient.

Cheers,
D

8

Its not that it is taking longer time, I meant it is not working in that way…

Maybe @moneta can help…

9

Hi Sandy,
I tried to draw your function and I get error in drawing it.

I replace it in the code below and now works.

void skew()
{
TF1 *f1 = new TF1("f1"," 2./(TMath::Sqrt(2*TMath::Pi()))*TMath::Gaus(x,[0],[1])*0.5 *(1.0 + erf( [2]*(x-[0])/sqrt(2)/[1] ) )",0.0,1000.0);
TH1D *h=new TH1D("h","h", 5000,0,1000);
f1->SetNpx(10000);    
f1->FixParameter(0,100.0);  // Mean             
f1->FixParameter(1,7.1);    // Sigma 
f1->FixParameter(2,5.0);    // Skewness

for(int i=0;i<10000;i++)
    h->Fill(f1->GetRandom());


h->Draw();


}
10

Hi @Dilicus

Thank you very much for the one you posted.

The one I posted was also working seperately.

Problem is that though it’s working seperately, when inserted into a event by event data analysis program, it freezes… Maybe because of calculating for too many events… e.g. 1,00,0000 events…

As @Danilo suggested I tried with a general C function. It is working but for that many events it freezes…

11

Hi @Danilo @Dilicus

When I run this function in ROOT 6.32.02, Ubuntu 24.04.1 LTS, gcc (conda-forge gcc 13.3.0-1) 13.3.0

I find this error:
cling::DynamicLibraryManager::loadLibrary(): libgsl.so.25: cannot open shared object file: No such file or directory
Error in TInterpreter::TCling::AutoLoad: failure loading library libMathMore.so for ROOT::Math::GSLIntegrator
cling::DynamicLibraryManager::loadLibrary(): libgsl.so.25: cannot open shared object file: No such file or directory

Warning in ROOT::Math::IntegratorOneDim::CreateIntegrator: Error loading one dimensional GSL integrator - use Gauss integrator

I have included:

#include “TSystem.h”
#include “Math/SpecFunc.h”
#include “Math/WrappedTF1.h”
#include “Math/GSLIntegrator.h”

and

gSystem->Load(“libMathMore”); inside the macro

but still it is showing the error.

Any help?