UPDATE 2
The question may be formulated as follows:
Is there any common probability distribution, like normal distribution, but which has sharp (or just sharper) edges? If yes, then I could approximate data with this distribution.
ORIGINAL
Suppose I have some histogram like following
and I want to normalize it, i.e. rescale values (in vertical dimension), say, to range [0..255].
The problem is that it is not well if I take just minimum and maximum values, since they probably contain outbreaks (like bin near 100 on picture).
Is there a way to calculate minimum and maximum in statistical way, something like 3 sigma or something?
I know I can just drop few maximal and minimal values as it done in sports.
UPDATE
This histogram is result of image evaluation in unknown (random) space, depending on color and other properties of image scanned. I want to scale it into [0..1] range to compare between each other.
Regard this as 1D grayscale image and I want to make it of uniform brightness and contrast.
You have hit on many of the issues. What you should do is not a mathematical question, and everything you have suggested is possible. A simple scaling by $\frac {255}{155}$ is a reasonable idea. For many purposes, the spike near $100$ wouldn't worry me-it isn't so far out of family that you lose information about the other bins. If it were three or four times higher than any other bin I would worry more. Dropping off the bottom, say taking $10$ counts input to $0$ output is possible, but if ratios between the bins are important you shouldn't do that. You can certainly calculate the mean and standard deviation-those are well defined formulas. Should you exclude points over $3 \sigma$ from the mean? If the distribution were normal (and most are not-they have longer tails) you would expect one real point in $370$ to be that far away and you have $255$. I would set the threshold higher for exclusion, if I did it at all.