Zero Modification of Hyperbolic Sine Distribution: Properties, Asymptotic Analysis and Applications

Abstract

This paper introduces the zero-modified hyperbolic sine (ZMHS) distribution, a new two-parameter discrete probability model. The ZMHS distribution is a more general and flexible extension of the original hyperbolic sine distribution, which contains hyperbolic sine, zero-truncated hyperbolic sine, zero-inflated hyperbolic sine, and zero-deflated hyperbolic sine as special sub-models. Key probabilistic properties of the ZMHS are derived. The proposed distribution offers greater flexibility than the hyperbolic sine distribution, as evidenced by its index of dispersion. Maximum likelihood estimation is proposed for inferring the parameters of the ZMHS distribution, and the asymptotic normality of the resulting estimators is established. Monte Carlo simulations are conducted to evaluate the finite-sample performance of the estimators, and the results confirm that the maximum likelihood estimators are consistent, with average estimates approaching true parameter values as sample size increases. Applications to two real datasets, along with comparative analyses involving existing count data models, demonstrates the flexibility of the ZMHS distribution and its potential as an alternative modeling approach.