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The discrete kernel method was developed to estimate count datadistributions, distinguishing discrete associated kernels based on theirasymptotic behaviour. This study investigates the class of discrete asymmetrickernels and their resulting non-consistent estimators, but this theoreticaldrawback of the estimators is balanced by some interesting features insmall/medium samples. The role of modal probability and variance of discreteasymmetric kernels is highlighted to help better understand the performance ofthese kernels, in particular how the binomial kernel outperforms otherasymmetric kernels. The performance of discrete asymmetric kernel estimators ofprobability mass functions is illustrated using simulations, in addition toapplications to real data sets.

On finite sample properties of nonparametric discrete asymmetric kernel estimators