Publication Date



Technical Report UTEP-CS-13-13a

To appear in Proceedings of the joint World Congress of the International Fuzzy Systems Association and Annual Conference of the North American Fuzzy Information Processing Society IFSA/NAFIPS'2013, Edmonton, Canada, June 24-28, 2013.


Some probability distributions (e.g., Gaussian) are symmetric, some (e.g., lognormal) are non-symmetric ({\em skewed}). How can we gauge the skeweness? For symmetric distributions, the third central moment C3 = E[(x - E(x))3] is equal to 0; thus, this moment is used to characterize skewness. This moment is usually estimated, based on the observed (sample) values x1, ..., xn, as C3 = (1/n) * ((x1 - E)3 + ... + (xn - E)3), where E = (1/n) * (x1 + ... + xn). In many practical situations, we do not know the exact values of xi. For example, to preserve privacy, the exact values are often replaced by intervals containing these values (so that we only know whether the age is under 10, between 10 and 20, etc). Different values from these intervals lead, in general, to different values of C3; it is desirable to find the range of all such possible values. In this paper, we propose a feasible algorithm for computing this range.

tr13-13.pdf (90 kB)
Original file: CS-UTEP-13-13