Fitting convolution of Gaussian and exponential

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:

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: The function was introduced here: (equation 9).