Selang Kepercayaan bagi Fungsi Intensitas Lokal Proses Poisson Periodik

Abstract

Proses stokastik merupakan salah satu bentuk model yang berkaitan dengan suatu aturan - aturan peluang. Proses stokastik dibedakan menjadi dua yaitu proses stokastik dengan waktu diskret dan proses stokastik dengan waktu kontinu. Salah satu bentuk khusus dari proses stokastik dengan waktu kontinu adalab proses Poisson periodik.

This thesis is concerned with confidence interval for the local intensity function of a periodic Poisson process. We consider the worst case when only a single realization of a periodic Poisson process available, which observed in an interval [0, n]. In this thesis estimation of the intensity function, as well as its statistical properties and asymptotic normality, are studied. An important thing for constructing a confidence interval is the asymptotic normality when the variance is estimated. Hence, an asymptotic normality with estimated variance is proved. Next, a confidence interval for the local intensity function of a periodic Poisson process is constructed. Furthermore, convergence of the probability that the estimated parameter is contained in this confidence interval, is proved. Finally, some computer simulations are carried out to check the behaviour of the asymptotic results for bounded samples.