statistical challenges

two distributions, with different means, the same sigma k1 X + k2 Y what are the k1 and k2

Approach 1: bare statistics Approach 2: hypothesis

Statistics sum xn /N +/- sigma

sigma < |M1X - M1Y|

Fuzzy Statistics (my approach) k1 X + k2 Y we do not answer the question , we use it

Numerical experiment X = rand(sigma, x) Y = rand(sigma, y) k1, k2 - known

Z = k1X + k2Y

Z~ => k1~ k2~ kmin / kmax << 1

We can make other hypothesis on the basis of this, without knowing the exact answer. That is fuzzy logic or fuzzy statistics.

Summary: Benefits of fuzzy statistics become obvious only in complex analytics, when one stage of reasoning depends on another. When hypothesis is what you measure directly, there are no benefits at all. Complex logic helps to filter bad hypothesis.