Understanding NBD Fit parameters

Newbie
1

ROOT Version: 6.32.04
Platform: WSL2 Ubuntu

Hello! I am performing an NBD fit to a charged hadron multiplicity curve. I define a fit function:

// Fitting function
TF1 *fist = new TF1("fist", "[0]*ROOT::Math::negative_binomial_pdf([1],[2],x)", 0, 60);

And then perform the fit with initial guesses for the variables.

// Input fit params
fist->SetParameter(0,1);		// normalisation parameter
fist->SetParameter(1,15);		// k - shape parameter
fist->SetParameter(2,0.5);		// p - probability parameter
// Perform fitting
hist->Fit("fist", "R0");

My doubts:

1 - As I understand the documentation, the negative_binomial_pdf accepts (k,p,n) respectively. Initially, I kept n as a parameter (by setting it to [3]). However, this did not work. After tweaking, I observed that setting n as x solves the issue. But I do not understand why?

2 - Is there a way to improve the fit further? Provided the plot below for reference.

a0f184a4-b2f1-490a-8c33-f217d2feecd4
a0f184a4-b2f1-490a-8c33-f217d2feecd4798×574 96.6 KB

Looking forward to any inputs since I am still new to ROOT. Thanks in advance!

2

Hello,

Thanks for the post and welcome to ROOT’s Community!
Interesting LEP fit.

  1. The fit procedure leads to estimates of the parameters values and uncertainties: how you set it up (what are variables or parameters is up to you)
  2. Hard to say… Depends on many factors: try to inspect the output of the minimizer to see if the fit converged correctly, for example.

Cheers,
D

3

Hi @Danilo,

Thanks for the response! I have a few follow-ups:

1 - To rephrase, do you perhaps know why using [0]*ROOT::Math::negative_binomial_pdf([1],[2],[3]) leads to the bad fit result shown below,

image
image1228×896 121 KB

… while using [0]*ROOT::Math::negative_binomial_pdf([1],[2],x) solves the issue?

As per the literature, using k,n as parameters for nCh curves is best. However, the only definition that works for me in ROOT requires n as an independent variable and k,p to be set.

image
image936×341 22.4 KB

(from a Los Alamos paper, can’t add a link as a new user)

2 - I will check this out, thank you.

Hope the question is clearer now. I want to build a qualitative understanding of how to use variables and parameters.

Cheers, Philip