Kekonvergenan MSE Penduga Kernel Seragam Fungsi Intensitas Proses Poisson Periodik dengan Tren Fungsi Pangkat
DOI:
https://doi.org/10.21512/comtech.v3i1.2403Keywords:
stochastic process, periodic Poisson process, kernel function, rank function trendsAbstract
The number of customers who come to a service center will be different for each particular time. However, it can be modeled by a stochastic process. One particular form of stochastic process with continuous time and discrete state space is a periodic Poisson process. The intensity function of the process is generally unknown, so we need a method to estimate it. In this paper an estimator of kernel uniform of a periodic Poisson process is formulated with a trend component in a rank function (rank coefficient 0 <b <1 is known, and the slope coefficient of the power function (trend) a> 0 is known). It is also demonstrated the convergenity of the estimators obtained. The result of this paper is a formulation of a uniform kernel estimator for the intensity function of a periodic Poisson process with rank function trends (for the case “a” is known) and the convergenity proof of the estimators obtained.
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References
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Wheeden, R.L., Zygmund. A. (1997). Measure and Integral: An Introduction to Real Analysis. New York: Marcell Dekker.
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