Asymptotic Distribution of an Estimator for Periodic Component of an Intensity Function as a Product of a Periodic Function with a Linear Trend of a Non-Homogeneous Poisson Process.

Abstract

In this thesis, estimation for periodic component of an intensity function as a product of a periodic function with a linear trend of a non-homogeneous Poisson process by using general kernel is discussed. It is considered the worst case, where there is only available a single realization of the Poisson process having intensity in the form of a periodic function multiplied by a linear trend, observed in an interval [0,n]. It is assumed that the period of the periodic component is known. An estimator has been constructed for the periodic component of the intensity function as a product of a periodic function with a linear trend of a Poisson process. Statistical properties of this estimator are also formulated. Finally, asymptotic normality of the estimator is also given.

Proses stokastik mempunyai peranan penting dalam berbagai bidang pada kehidupan sehari-hari. Sebagai contoh, proses kedatangan pelanggan pada suatu pusat pelayanan dapat dijelaskan dengan proses stokastik. 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 adalah proses Poisson periodik. Proses Poisson periodik adalah suatu proses Poisson dengan fungsi intensitas berupa fungsi periodik.