Fitting a truncated normal (Gaussian) distribution

How to fit a truncated distribution

Matlab does not allow to say that a distribution which we fit to a dataset is truncated.
In case of a Gaussian distribution, Matlab just calculates the mean and sigma and uses them as the paramters of a pdf, but this does not work if the distribution is cutted from one side, e.g. when you don't have measurements less than some detection limit. Then fitted distribution will be shifted.
Here I give an small example how to perform fitting in this case.