Abstract

The negative binomial distribution is known as the most commonly used distributions in the count data study with over-dispersed characteristics. Accordingly, a negative binomial regression model is introduced, in which the average number of failures is considered as an exponential function. This paper aims to find an optimal design for this model based on a predictor variable. Given the need for a suitable criterion to obtain an optimal design, this paper uses the D-optimality criterion, known as a function based on the Information matrix. Also, considering the dependence of this criterion on the unknown parameters of the model, the Bayesian approach is intended to eliminate this dependence, with the Bayesian design resulting from the desired process.