Landau distribution properties in RooFit (ROOT?)

[adavid]

Continuing the discussion from Chained PDF definitions: against what would be expected from a stable distribution like the Landau, the convolution of Landau(mpv, sigma) with Landau(mpv, sigma) in RooFit is not yielding the same result as Landau(2mpv, 2sigma). I wonder if this is related to numerical issues with the Landau implementation in ROOT/RooFit or with something else.

[oshadura]

perhaps @moneta or @vcroft can help here?

Thank you,
Oksana.

[moneta]

Hi,

I think the issue is due to a misunderstanding of the parameter of the Landau distribution.
For a Landau(x, m, s) m is not the MPV and the location of the maximum of the distribution, it is just a location parameter. For example for m=0 the maximum of the Landau is -0.22.
We have only an implementation of Landau(t) which is transformed as Landau( x,m,s) with t = (x-m)/s
See more on
https://www.sciencedirect.com/science/article/pii/0010465584900857

for the Landau implementation

Lorenzo

[adavid]

Hi Lorenzo,

So your point is that the underlying univariate approximation is such that the stable distribution properties are violated?

Thanks,

Andre