Constructing Stieltjes classes for M-indeterminate absolutely continuous probability distributions

Abstract

If P is a moment-indeterminate probability distribution, then it is desirable to present explicitly other distributions possessing the same moments as P. In this paper, a method to construct an infinite family of probability densities - called the Stieltjes class - all with the same moments is presented. The method is applicable for densities with support (0, infinity) which satisfy the lower bound: f(x) >= A exp{-ax(alpha)} for some A > 0, a > 0 and some alpha is an element of(0, 1/2):