Count data represents a number of defined events that occur within a specific time frame for explanatory variables in the form of integers, and discrete distributions are among the probability distributions that use count data. The most famous of these distributions is the Poisson distribution. However, sometimes a change in the pattern of the random variable period may occur, such as the absence of the zero value, which requires finding a distribution that fits such a change, and that is the Zero Truncated Poisson Distribution (ZTPD).

       This research aims to find a suitable model for the effect of non-zero value of data on any phenomenon and to use it to build a Zero Truncated Poisson Regression Model. This is done by selecting the best method out of three methods: Gauss-Newton (GN), Iteratively re-weighted least squares (IRWLS), and the Newton-Raphson algorithm method embedded in Maximum Likelihood (N-RAMEML), using the Mean Square Error (MSE) criterion, by simulating the Monte Carlo method using the R language program. This is done by changing different factors such as sample size (30, 70, 100, and 150) and the number of explanatory variables, repeating each experiment 1000 times. The study showed that the IRWLS method outperforms the N-RAMEML and GN methods.

Paper type: Research paper