The Zero Inflated Negative Binomial - Shanker Distribution and Its Application to HIV Exposed Infant Data

Motivated by HIV exposed infants (HEI) sero-conversion data, we provide an extension of Zero-inflated Negative Binomial (ZINB) distribution to Zero Inflated Negative Binomial - Shanker (ZINB-SH) distribution. In this setting the ZINB-SH, distribution provides an alternative to the Poisson-Shanker distribution in particular, when data exhibits over dispersion brought by excess zeros. The HIV Exposed infant data is characterized by both structured and non-structured zeroes which makes the feature ideal in this context. We describe the properties of ZINB-SH distribution and estimate its parameters. Extensive simulations were conducted and the results in terms of goodness-of-fit, compared to the standard Negative Binomial, Shanker, Zero-Inflated Negative Binomial and Negative Binomial –Shanker distributions. The ZINB-SH distribution is competitive under different settings of simulation and does well as sample size increases. To validate the distribution, we apply real typical HIV-Infant exposed data