In this paper we study the parameterized complexity of approximating theparameterized counting problems contained in the class $\#W[P]$ ,the parameterized analogue of $\#P$
,the parameterized analogue of $\#P$ . We prove a parameterized analogue of afamous theorem of Stockmeyer claiming that approximate counting belongs tothe second level of the polynomial hierarchy.
. We prove a parameterized analogue of afamous theorem of Stockmeyer claiming that approximate counting belongs tothe second level of the polynomial hierarchy.