The Zero Inflated Negative Binomial - Shanker distribution and its application to HIV exposed infant data

Date
2020
Authors
Kibika, Stella Andia
Journal Title
Journal ISSN
Volume Title
Publisher
Strathmore University
Abstract
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.
Description
A Thesis submitted in partial fulfillment of the requirements for the Degree of Master of Science in Statistical Sciences (MSc. SS) at Strathmore University
Keywords
Zero Inflated Negative Binomial - Shanker (ZINB - SH), HIV exposed infants, Data
Citation