Poissonmodel
Poissonmodel refers to a statistical framework for modeling count data where the response variable Y_i follows a Poisson distribution with mean λ_i. In its regression form, the mean is modeled as a function of explanatory variables X_i, often via a log link: log(λ_i) = X_iβ. When an exposure or observation window t_i is present, an offset term log(t_i) can be added so that λ_i = t_i exp(X_iβ), representing the expected count per unit exposure.
Assumptions include independence of observations and that the variance equals the mean (var(Y_i) = λ_i). The likelihood
Model checking uses residuals and goodness-of-fit measures such as deviance and Pearson chi-square. A common issue
Extensions include zero-inflated Poisson and hurdle models for excess zeros. Poissonmodels are widely used in epidemiology,