Robust parameter estimation for one-inflated positive Poisson Lindley distribution under the presence and absence of outliers with applications to crime data

The one-inflated positive Poisson Lindley model hasbeen recently introduced as an alternative in modelling positive count data with a large number of ones: a phenomenon known as one-inflation. In the presenceof oneinflation, this model has a high tendency to be influenced by outliers, making usual parameter estimatons to be less robust. Hence, several estimators: maximum likehood, method of moments, ordinary least squares,weighted least squares, Cram & eacute;r-Von Mises, modified Cram & eacute;r-Von Mises (MCVM) and maximum product of spacing (MP;S) for the parameters of the model are also proposend ainvestigated in terms of unbiasedness, consistency and joint efficiency under the presence and absence of outliers. When the outliers are absent, the MPS estimatoris the best estimator and when the outliers are present, the MCVM estimator is the best estimator. Model fittingsto two real datasets with one-inflation and outliers supporte thsimulation results and conclude that the MCVM estimator is the best estimator. Based on the best robust estimator,he population size of the number of offenders aswell as the likelihood of arrests were estimated.