Pendugaan Fungsi Intensitas Proses Poisson Periodik dengan Tren Fungsi Pangkat Menggunakan Metode Tipe Kernel

Authors

  • Ro’fah Nur Rachmawati Bina Nusantara University

DOI:

https://doi.org/10.21512/comtech.v2i1.2783

Keywords:

stochastic process, periodic Poisson process, Kernel function, rank function trend

Abstract

Stochastic process has an important role in many areas in everyday life, including the customer service process. The number of customers who come to a service center will be different for each particular time. A special form of stochastic process with continuous time and discrete state space is periodic Poisson process, which is a Poisson process with an intensity function of a periodic function. However, on the stochastic modeling of a phenomenon by a periodic Poisson process, the intensity function of the process is generally unknown. Therefore, a method is needed to infer the function. In this article, a Kernel estimator is formulated from a periodic Poisson process with a trend component in a rank function, which is divided into two cases; the identified rank function coefficient and the unidentified rank function coefficient.

 

Dimensions

Plum Analytics

References

Ghahramani, S. (2005). Fundamental of Probability, (3rd ed.). New York: Prentice Hall.

Hogg, R. V. & Craig, A. T. (2005). Introduction to Mathematical Statistics, (5th ed.). New Jersey: Prentice Hall, Engelwood Cliffs.

Mangku, I. W. (2001). Estimating the Intensity of a Cyclic Poisson Process. Amsterdam: University of Amsterdam.

Mangku, I. W. (2006). Asymptotic Normality of a Kernel-type Estimator for the Intensity of a Periodic Poisson Process. Journal of Mathematics and Its Applications, 5 (2), 13-22.

Mangku, I. W. (2006). Weak and Strong Convergence of a Kernel-type Estimator for the Intensity of a Periodic Poisson Process. Journal of Mathematics and Its Applications, 5 (1), 1-12

Rachmawati, N. R. (2008). Sifat-sifat Statistika Penduga Fungsi Intensitas Proses Poisson Periodik dengan Tren Fungsi Pangkat. Skripsi tidak diterbitkan. Bogor: Fakultas Matematika dan Ilmu Pengetahuan Alam Institut Pertanian Bogor.

Wheeden, R. L., Zygmund, A. (1997). Measure and Integral: An Introduction to Real Analysis. New York: Marcell Dekker.

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Published

2011-06-01

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