Strange behavior of TF1 with ROOT::Math::negative_binomial_pdf

ROOT
1

Dear rooters:

I am trying to generate a bunch of negative binomial distribution with TF1 using “r” and “p” parameters that I have extracted from a set of data. From the data I extract a mean and a variance term that I use to calculate “r” and “p” and construct the functions. I just took one example where I have a mean of 1.63 from where I infer an r =18.9242 and a p=0.920519. Now the problem is that I create the TF1 using ROOT::Math::negative_binomial_pdf(x[0],0.920519,18.9242) and when I plot this function I get a mean of 2.13252 (from Mean(min,max)) and the function looks like shifted to the right (it never reaches x=0). I have cross-checked my calculation of the mean using std::negative_binomial_distribution<int> d(round(18.9242),0.920519) and the result is correct (1.63774). I am not sure what I am doing wrong. I attach a simple macro that illustrates the problem.

Thank you very much in advance
F.
test_NBD.C (2.0 KB)

Please provide the following information:

ROOT Version 6.06/06):
Platform, compiler (Ubuntu 16 gcc and Mac El Capitan):

2

Hi,

I think the problem is due to the fact that the negative binomial distribution is an integer distribution.
TF1::GetRandom makes some interpolation inside and generate values assuming a continuous distribution.
Converting the TF1 to a TH1D and using correct binning (having bin center equal to integer values fixes the problem), as you see in the attached macro.

However I would use directly the function NegativeBinomial of ROOT::Math::GSLRandom.

ROOT::Math::GSLRngMT r; 
r.NegativeBinomial(0.920519,18.9242);

Lorenzo
test_NBD.C (2.0 KB)

3

Hi,

Thank you very much, I figured it out the way you mention. And it is nice to see that there is an alternative and simpler way to sample from the distribution.

Cheers
F.