Estimation of the Zero-Truncated Poisson Regression Model using Iteratively Reweighted Least Squares Method with Application: and Some Distribution Properties

Abstract

The Zero Truncated Poisson Distribution (ZTPD) is a special case of the Poisson distribution that occurs when the Poisson distribution is devoid of zero values for certain phenomena, resulting in a change in its probability function and statistical properties. The aim of this study is to find a modeling approach that accommodates the impact of data values without the zero value for any phenomenon and to use it to build a Zero Truncated Poisson Regression Model (ZTPRM) using the Iteratively Reweighted Least Squares (IRWLS) method. This model is used to estimate the regression model and parameters for the Zero Truncated Poisson Distribution, with some distribution properties mentioned. In the applied side, a sample of 68 patients with renal failure undergoing renal dialysis at Al-Karama Hospital/Life Kidney Center was drawn.