The Numerical Simulation for Asymptotic Normality of the Intensity Obtained as a Product of a Periodic Function with the Power Trend Function of a Nonhomogeneous Poisson Process

Ikhsan Maulidi, Mahyus Ihsan, Vina Apriliani

Abstract


In this article, we provided a numerical simulation for asymptotic normality of a kernel type estimator for the intensity obtained as a product of a periodic function with the power trend function of a nonhomogeneous Poisson Process. The aim of this simulation is to observe how convergence the variance and bias of the estimator. The simulation shows that the larger the value of power function in intensity function, it is required the length of the observation interval to obtain the convergent of the estimator.


Keywords


Poisson Process; Intensity Function; Power Trend Function; Asymptotic Normality.

Full Text:

PDF

References


Dudley, R. (1989). Real analysis and probability. Wardswort & Brooks.

Erliana, W., Mangku, I. W., & Sumarno, H. (2014). Estimating the intensity obtained as product of a periodic function with the power function trend of a nonhomogeneous poisson process. Far East Journal of Mathematical Sciences, 90(2), 163–172.

Helmers, R., Wayan Mangku, I., & Zitikis, R. (2003). Consistent estimation of the intensity function of a cyclic Poisson process. Journal of Multivariate Analysis, 84(1), 19–39. https://doi.org/10.1016/S0047-259X(02)00008-8

Hogg, R., Craig, A., & Kean, J. M. (2005). Introduction to mathematical statistics (6th ed.). Prentice Hall, Upper Saddle River.

Mahmud, T., Hasan, M., Chakraborty, A., & Roy-chowdhury, A. K. (n.d.). Tahmida Mahmud University of California , Riverside. 2016 IEEE International Conference on Image Processing (ICIP), 3339–3343. https://doi.org/10.1109/ICIP.2016.7532978

Mangku, I. W. (2011). Estimating the intensity obtained as the product of a periodic function with the linear tren of a non-homogeneous Poisson process. Far East Journal of Mathematical Science, 51, 141–150.

Mangku, I. W., Budiarti, R., & Taslim, C. (2013). Estimating the intensity obtained as the product of a periodic function with the quadratic trend of a non-homogeneous poisson process. Far East Journal of Mathematical Science, 82(1), 33–44.

Maulidi, I. (2015). Kekonsistenan kuat dan sebaran asimtotik penduga intensitas berupa fungsi periodik kali tren fungsi pangkat proses poisson nonhomogen. IPB University.

Maulidi, I., Mangku, I. W., & Sumarno, H. (2015). Strong consistency of kernel-type estimator for the intensity obtained as the product of a periodic function with the power function trend of non-homogeneous poisson process. British Journal of Applied Science and Technology, 9(4), 383–387.

Serfling, R. (1980). Approximation theorems of mathematical statistics. J Wiley.

Sumiati, I., Rahmani, U., & Supian, S. (2019). Application of the nonhomogeneous poisson process for counting earthquakes. 127(January 2016), 163–176.

Tse, K.-K. (2014). Some applications of the poisson process. Applied Mathematics, 05(19), 3011–3017. https://doi.org/10.4236/am.2014.519288




DOI: http://dx.doi.org/10.24042/djm.v3i3.6374

Refbacks

  • There are currently no refbacks.


Copyright (c) 2020 Desimal: Jurnal Matematika

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

  Creative Commons License
Desimal: Jurnal Matematika is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.