Circularly shifted histogram: Modular addition (or subtraction) of a constant value to all data points.
Maxima, Minima, etc. might not be a unique value, therefore can't be used.
Edit: Let me express myself in detail -
I have data that I will use to plot a histogram with appropriate bin size (bin size can be anything). Now data can be modulo-added or subtracted by some constant - causing the histogram to get circularly shifted.
I need some way to define a point in the histogram (bin index: x-axis value) so that I would be able to determine that point for all circularly shifted histograms.
e.g. Suppose there is a unique maximum of the histogram. Now, the histogram is circularly shifted by a const value. How would I find the magnitude of the shift? Calculate the maximum value of the new histogram and subtract the old index from the new one. Point of the maximum value of the histogram was my desired histogram index. But since uniqueness of the maximum is not guaranteed, I need to find a different index-point.
In general, the answer is no. For example, if this is your histogram, there are multiple shifts that give the same result.