Some consequences of a characterization theorem based on truncated moments

Let X be an arbitrary real-valued random variable and let g and h be two real functions such that E (g(X)| X ≧x) and E (h(X) | X ≧x) are defined. It was shown that under relatively mild conditions the distribution of X is uniquely determined by the functions g, h and ?=E (g(X) | X≧x)/E(h(X) | X≧x) (GLANZEL, 1987). In the present paper we show that this characterization is stable in the sense of weak convergence. Some consequences of this stability theorem and the above characterization are discussed