  The discrete kernel method was developed to estimate count data
distributions, distinguishing discrete associated kernels based on their
asymptotic behaviour. This study investigates the class of discrete asymmetric
kernels and their resulting non-consistent estimators, but this theoretical
drawback of the estimators is balanced by some interesting features in
small/medium samples. The role of modal probability and variance of discrete
asymmetric kernels is highlighted to help better understand the performance of
these kernels, in particular how the binomial kernel outperforms other
asymmetric kernels. The performance of discrete asymmetric kernel estimators of
probability mass functions is illustrated using simulations, in addition to
applications to real data sets.
