  Following a strategy recently developed by Ivan Nourdin and Giovanni Peccati,
we provide a general technique to compare the tail of a given random variable
to that of a reference distribution. This enables us to give concrete
conditions to ensure upper and/or lower bounds on the random variable's tail of
various power or exponential types. The Nourdin-Peccati strategy analyzes the
relation between Stein's method and the Malliavin calculus, and is adapted to
dealing with comparisons to the Gaussian law. By studying the behavior of the
solution to general Stein equations in detail, we show that the strategy can be
extended to comparisons to a wide class of laws, including many Pearson
distributions.
