  In Mombeni et al. (2019), Birnbaum-Saunders and Weibull kernel estimators
were introduced for the estimation of cumulative distribution functions
(c.d.f.s) supported on the half-line $[0,\infty)$. They were the first authors
to use asymmetric kernels in the context of c.d.f. estimation. Their estimators
were shown to perform better numerically than traditional methods such as the
basic kernel method and the boundary modified version from Tenreiro (2013). In
the present paper, we complement their study by introducing five new asymmetric
kernel c.d.f. estimators, namely the Gamma, inverse Gamma, lognormal, inverse
Gaussian and reciprocal inverse Gaussian kernel c.d.f. estimators. For these
five new estimators, we prove the asymptotic normality and we find asymptotic
expressions for the following quantities: bias, variance, mean squared error
and mean integrated squared error. A numerical study then compares the
performance of the five new c.d.f. estimators against traditional methods and
the Birnbaum-Saunders and Weibull kernel c.d.f. estimators from Mombeni et al.
(2019). By using the same experimental design, we show that the lognormal and
Birnbaum-Saunders kernel c.d.f. estimators perform the best overall, while the
other asymmetric kernel estimators are sometimes better but always at least
competitive against the boundary kernel method.
