Getting 16 bit image statistics in Photoshop
A lot of tools do this by default (even matlab's image processing tools for the most part). I'd load the image up in matlab and use the hist, std, mean, etc function by treating the image as a vector. Tools like EnvI also handle 16 bit images properly.

The matlab/octave code would be roughly as follows (assuming 16 bit greyscale png):

img=double(imread('image.png'));
mean(img(:))
std(img(:))
hist(img(:),number of bins)