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I've three circles as seen in the image.

Source: http://www.picpaste.com/Quantify-PwdfQxLB.png [Broken]

Within the innermost circle is a point. I'd like to determine the likelihood, or probability, that this point belongs to the innermost circle, the middle-circle, and outermost circle.

Now, this point -- as can be seen in the image -- is very near the boundary of the innermost circle. Also, it is near the boundary of the middle-circle, so one might assume that the probability of being in each of the three circles is APPROXIMATELY (.33, .33, .33).

If we were to translate the point and shift it into the center of the innermost circle, I'd assume the distribution to be (1.0, 0.0, 0.0), for the point would lie in the middle of the innermost circle.

For another example, if I were to translate the point to the left a little, I'd probably see the distribution to be (0.45, 0.35, 0.2), respectively.

Is there a way to quantify, or determine, the likelihood that this point belongs to a specific circle in this example?

Thank you.

Trecius

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# Measuring Membership, or Likelihood, of given Point

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