I need to fit the convolution of a Gaussian distribution with an exponential distribution to a histogram.
Is there an analytical expression for such a function? Does it have a name (=> does Root have a built-in function for this?)? Is the Landau distribution physically related?
As far as I know there is no built-in function for this. Fortunately I think you can do the convolution analytically by hand (it has a closed-form expression). With that, you can just define a C++ function that you can use to make a TF1 for fitting: http://root.cern.ch/root/html/TF1.html#F3
The Landau distribution is only related in that it can look like a biased Gaussian with a hard cutoff on one end, but I wouldn’t use it as a substitute because it has much different behavior. It has infinite mean & standard deviation for example, which is very different than a Gaussian.
If you do want a general Gaussian-like function with an asymmetry and hard cutoff, I would recommend a Novosibirsk function. RooFit has one built-in, but I ended up writing my own: https://bazaar.launchpad.net/~jfcaron/+junk/Proto2BeamTest2/view/head:/garfield_results/novosibirsk.C The function was introduced here: http://www.sciencedirect.com/science/article/pii/S0168900299009924 (equation 9).