Consistent second-order discrete kernel smoothing using dispersed Conway–Maxwell–Poisson kernels

The histogram estimator of a discrete probability mass function often exhibits undesirable properties related to zero estimation both within the observed range counts and outside into tails distribution. To circumvent this, we formulate novel second-order kernel smoother based on recently developed mean-parametrized Conway--Maxwell--Poisson distribution which allows for over- under-dispersion. Two automated bandwidth selection approaches, one simple minimization Kullback--Leibler divergence another more computationally demanding cross-validation criterion, are introduced. Both methods exhibit excellent small- large-sample performance. Computational results simulated datasets from target distributions illustrate flexibility accuracy proposed method compared existing smoothed unsmoothed estimators. is applied modelling somite in earthworms, number development days insect pests Hura tree.