This paper introduces two new nonparametric estimators for probability density functions which have support on the non-negative half line. These kernel estimators are based on some inverse Gaussian and reciprocal inverse Gaussian probability density functions used as kernels. We show that they share the same properties as those of gamma kernel estimators: they are free of boundary bias, always non-negative, and achieve the optimal rate of convergence for the mean integrated squared error. Extensions to regression curve estimation and hazard rate estimation under random censoring are briefly discussed. Monte Carlo results concerning finite sample properties are reported for different distributions.

Keywords : Boundary bias, Inverse Gaussian kernel, Reciprocal inverse Gaussian kernel, Gamma kernel, Variable kernel, Density estimation.

JEL : C13, C14.