MSc.SS Theses and Dissertations

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The Zero Inflated Negative Binomial - Shanker distribution and its application to HIV exposed infant data
(Strathmore University, 2020) Kibika, Stella Andia
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. We review the classical Poisson, and negative binomial distribution when applying count data and there zero- Inflated versions. After reviewing the conceptual and computational features of these methods, we generate a new extension which is intrinsically a combination of Zero- Inflated Negative Binomial and Shanker 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-_t, 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 Exposed Infant data.