Estimation of The Intensity Function of Non-Homogeneous Poisson Process Using Non-Parametric Density Estimation Methods

Amira, Tarik A.; Habib, Mohamed E.; Al-Harby, Abdullah

doi:10.21608/esju.1991.315029

Estimation of The Intensity Function of Non-Homogeneous Poisson Process Using Non-Parametric Density Estimation Methods

Document Type : Original Article

Authors

¹ Dep. of Statistics, Faculty of Economics, Cairo University, Egypt

² Dep. of Statistics , Faculty of Commerce, Al-Azhar University, Egypt

³ Dep. of Statistics, Faculty of Science, K.A.University, Jeddah, Saudi Arabia

10.21608/esju.1991.315029

Abstract

This paper presents a contribution in the non-parametric estimation of the intensity function of non-homogeneous Poison process from the practical point of view. The cumulative distribution functions of the times of successive events are obtained and the method of Monte Carlo is used to simulate the Poison process with intensity function λ(t) = ae^(-bt) The authors selected samples of different sizes from this process and the data of these samples is used to estimate the intensity function by the histogram method and the kernel method with different kerns. The figures of estimates are obtained and the measure of discrepancy D = supt|λ^(t) - λ(t)| is calculated.

Keywords