SGJ, thanks, I'm kinda "debdey" by nature and some take offense at me. Glad we can talk openly.
Distribution is a very different meaning/definition to me in this case. I'm using the statistical definition of how a statistic (in this case pellet hits per sq inch or sq inches per pellet hit) varies with pattern radius from center to edge. No pellet will hit exactly center, so, the hits/sq in at center is zero. However, as you move even a little off center, the hits/sq in will go to the maximum and then taper off. Shotgun patterns follow the Rayleigh distribution - remember the more famous Normal distribution frequently refered to as the bell curve? Well, the Rayleigh looks like the bell except that it takes a very sharp dip from max to zero at the center of the pattern circle. Remember "center thickening?" That is slang for the high values of the distribution near the center. The difference between "center thickening" and the "Rayleigh distribution" is that the distribution gives you hits /sq in which can be related to lethalness of the pattern. Matter of fact, you get a very good picture of the diameter of the effective part of your pattern as opposed to the overall diameter of the pattern. "Central thickening" simply tells you there is more shot per sq. in. toward the middle of the pattern than toward the edge. Remember I said the pattern can be predicted for greater and lesser ranges? Well, that is the beauty of this method.
