Probabilistic Frontier Regression Models for Count Type Output Data

This paper proposes a Conway-Maxwell-Poisson (COM-Poisson) probabilistic frontier regression model for count type output data addressing the dispersion in the data. We consider some of the outcomes as desired outcomes or ‘interest class’, and a change in the probability of output falling into this class is attributed to the decrease in the decision-making unit’s technical efficiency (TE). A measure for TE is proposed to determine the deviations of individual units from the probabilistic frontier of ‘interest class’. Simulation results show that the true distribution of the efficiency component matches with its predictive distribution. The proposed model is applied to evaluate the TE of Indian states in dealing with different crimes.