Estimating third central moment C3 for privacy case under interval and fuzzy uncertainty
Ali Jalal-Kamali, Владик Крейнович · 2013
Some probability distributions (e.g., Gaussian) are symmetric, some (e.g., lognormal) are non-symmetric (skewed). How can we gauge the skeweness? For symmetric distributions, def 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 · Σi=1n(xi- E)3, where E =def1/n · Σi=1nxi. In many practical situations, we do not know the exact values of x%. 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.