RooFit: Examples of supported PDFs

Hello,

Is there a place which shows a sample shape of all the PDFs that Roofit supports? Or is there a simple way to make these? I don’t see this in the doumentation. I would just like to see and overview of the different PDF shapes. Maybe there’s a better PDF I could use but have no idea, but I’m also just curious.

james

Hi,

There is a short overview of the basic shapes in the RooFit manual of the available shapes. I’m working on bring this up to date for the next update of the manual since there are a couple of new ones.

But in general you should consider these basic shapes as starting points. Any variable of a p.d.f can be replaced by a function turning it into a more complex shape (i.e. F(x,p) --> F(x,p(y,a)) = F(x,y,a)).

Is there are particular problem for which you need a (better) p.d.f?

Wouter

I am fitting a distribution with a triple-gaussian, and I’d like to reduce the number of free parameters. I’ve tried a crystalball, bifurcated gaussian, but I was just wondering what other shapes there were, so that I might just do some exploring.

james

Hi,

That’s just for your signal shape? In general, fitting a triple Gaussian is hard because of strong correlations between the various width and fraction parameters. You can reduce this somewhat by e.g. reparameterizing sigma2–>sigma1sf2 and sigma3 = sigma2sf2 and choosiing lower limits on sf2, sf3 >=1 but it remains tricky.

In general, basic shapes for signal-like components are

RooGaussian - self explanatory
RooBifurGauss - self explanatory
RooCBShape CrystalBall - Gaussian with exponential tail glued on
RooLandau - self explanatory
RooNovosibirsk - The Novosibirsk function is defined as f(m)=A exp(-0.5{ln^2[1+Lambda tau·(m-m0)]/tau^2+tau^2}), where Lambda=sinh(tau sqrt(ln4))/(sigma tau sqrt(ln4)), the peak position is m0, the width is sigma, and tau is the tail parameter.
RooBukinpdf (variation on Novosibirsk, link to documentation in class code)
RooBreitWigner - self explanatory
RooVoigtian - BW (x) Gaussian

But your choice should depend somewhat on what shape you expect it a priority to have…

Wouter