In this paper, we consider the problem of estimating the number of times an air quality
standard is exceeded in a given period of time. A non‐homogeneous Poisson model is
proposed to analyse this issue. The rate at which the Poisson events occur is given by a rate
function λ (t), t≥ 0. This rate function also depends on some parameters that need to be
estimated. Two forms of λ (t), t≥ 0 are considered. One of them is of the Weibull form and the
other is of the exponentiated‐Weibull form. The parameters estimation is made using a …