Stieltjes Moment Problem

The Stieltjes Moment Problem involves determining whether there exists a probability distribution (a way to assign weights or probabilities to different values) on the non-negative real numbers (0 to infinity) such that its moments—expected values of powers of the variable—match a given sequence. In essence, it questions if a set of data points can come from a real, consistent distribution supported on the positive real line. Finding such a distribution confirms the moments are "realizable," and solving the problem involves understanding the conditions under which this is possible.