Computing Higher Central Moments for Interval Data

Higher central moments are very useful in statistical analysis: the third moment M3 characterizes asymmetry of the corresponding probability distribution, the fourth moment M4 describes the size of the distribution’s tails, etc. When we know the exact values x1, . . . , xn, we can use the known formulas for computing the corresponding sample central moments. In many practical situations, however, we only know intervals x1, . . . ,xn of possible values of xi; in such situations, we want to know the range of possible values of Mm. In this paper, we propose algorithms that compute such ranges. 1 Formulation of the Problem Higher moments are important. In engineering and science, when we have n measurement results x1, . . . , xn, traditional statistical approach (see, e.g., [5, 21]) usually starts with computing their (sample) average E = x̄ = x1 + . . . + xn n and their (sample) variance V = (x1 − E) + . . . + (xn − E) n .