  We study the Tauberian relations between the moment generating function (MGF)
and the complementary cumulative distribution function of a random variable
whose MGF is finite only on part of the real line. We relate the right tail
behavior of the cumulative distribution function of such a random variable to
the behavior of its MGF near the critical moment. We apply our results to an
arbitrary superposition of a CIR process and the time-integral of this process.
