  We consider the nonparametric estimation of the univariate heavy tailed
probability density function (pdf) with a support on $[0,\infty)$ by
independent data. To this end we construct the new kernel estimator as a
combination of the asymmetric gamma and weibull kernels, ss. gamma-weibull
kernel. The gamma kernel is nonnegative, changes the shape depending on the
position on the semi-axis and possess good boundary properties for a wide class
of densities. Thus, we use it to estimate the pdf near the zero boundary. The
weibull kernel is based on the weibull distribution which can be heavy tailed
and hence we use it to estimate the tail of the unknown pdf. The theoretical
asymptotic properties of the proposed density estimator like bias and variance
are derived. We obtain the optimal bandwidth selection for the estimate as a
minimum of the mean integrated squared error (MISE). Optimal rate of
convergence of the MISE for the density is found.
