The Confidence Interval for the Periodic Intensity Function in the Presence of Power Function Trend on the Nonhomogeneous Poisson Process

The nonhomogeneous Poisson process is one of the most widely applied stochastic processes. In this article, we provide a confidence interval of the intensity estimator in the presence of a periodic multiplied by trend power function. This estimator's confidence interval is an application of the formulation of the estimator asymptotic distribution that has been given in previous studies. By using the asymptotic theorem, the distribution was derived in the form of a confidence interval for the intensity function. In addition, constructive proof of the convergent in probability has been provided for all power functions. The results of this study contribute to the study of statistical analysis of the estimators that have been formulated previously.