Pendugaan Fungsi Nilai Harapan pada Proses Poisson Periodik Majemuk dengan Tren Fungsi Pangkat

Abstract

This manuscript is concerned with consistent estimation of the mean function of a compound cyclic Poisson process with power function trend. The cyclic component of intensity function of this process is not assumed to have any parametric form, but its period is assumed to be known. The slope of the power function trend is assumed to be positive, but its value is unknown. The main problems of this manuscript are constructing an estimator of this mean function, proving consistency of this estimator, and determining the rate of convergence to zero for the bias, variance, and mean squared error of this estimator, when the length of the observation time interval indefinitely expands.