Simultaneous Confidence Intervals for Parameters of Zero-Inflated Negative Binomial Model and Hurdle Negative Binomial Model

Count data sets in many real-world scenarios exhibit zero-inflation, characterised by an excessive zero counts. Zero-inflated negative binomial (ZINB) and hurdle negative binomial (HNB) models are commonly applied to handle this issue, particularly in the presence of overdispersion. The hurdle model distinguishes between zero and positive counts, applying a truncated count model to the non-zero values while the ZINB model posits two separate processes: one generating only zeros and the other producing counts that follow a negative binomial distribution. This study focuses on obtaining estimators of the parameters of both ZINB and HNB models using method of moments, method of moments with proportion estimator and maximum likelihood method. The estimators are compared with respect to relative bias and mean squared error (MSE). Further, approximate simultaneous <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msup> <mml:mi>T</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> confidence intervals for the parameters of these models are constructed by obtaining variance-covariance matrix using inverse of Fisher information matrix, inverse of Fisher information matrix based on profile likelihood obtained by eliminating the nuisance parameter <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>π</mml:mi> </mml:math> (inflation parameter) and using parametric bootstrap method. Monte-Carlo simulations are conducted to evaluate the performance of these methods, in terms of coverage probabilities and the length of the confidence intervals. The study analyses number of cases registered for violation of Essential Commodities Act by applying ZINB model.