We consider semiparametric asymmetric kernel density estimators when the unknown density has support on [ 0, infinity) We provide a unifying framework which contains asymmetric kernel versions of several semiparametric density estimators considered previously in the literature This framework allows us to use popular parametric models in a nonparametric fashion and yields estimators which are robust to misspecification We further develop a specification test to determine if a density belongs to a particular parametric family The proposed estimators outperform rival non- and semiparametric estimators in finite samples and are simple to implement We provide applications to loss data from a large Swiss health insurer and Brazilian income data.