Measure degree of changes between 2 histograms

I have 2 images, reference and distorted one. The distorted one had been changed in the way, that its histogram was:

- stretched or unstreched and/or

- shifted.

The type and the degree of this operation is unknown. What is most reliable (and computational undemanding, if possible) method to measure degree of those distortions, i.e. histogram "stretchiness" and "stretchiness"?