ASYMPTOTIC DISTRIBUTIONS OF ESTIMATORS FOR THE MEAN AND THE VARIANCE OF A COMPOUND CYCLIC POISSON PROCESS

DOI: https://doi.org/10.30598/barekengvol20iss1pp0453-0464
Keywords: Asymptotic distribution, Compound cyclic Poisson process, Intensity function

Abstract

A stochastic process has an important role in modeling various real phenomena. One special form of the stochastic process is a compound Poisson process. A compound Poisson process model can be extended by generalizing the corresponding Poisson process. One of them is using a cyclic Poisson process. Our goals in this research are to determine the asymptotic distribution of the estimator for the mean and the variance of this process. In this paper, the problems of estimating the mean function and the variance function of a compound cyclic Poisson process are considered. We do not assume any parametric form for the intensity function except that it is periodic. We also consider the case when only a single realization of the cyclic Poisson process is observed in a bounded interval. Consistent estimators for the mean and variance functions of this process have been proposed in respectively. This paper introduces a set of novel theorems that, to the best of our knowledge, are not available in the existing literature and contribute original results to the field. Asymptotic distributions of these estimators are established when the size of the observation interval indefinitely expands. Asymptotic distributions of  and  are, respectively and as .

 

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Published
2025-11-24
How to Cite
[1]
I. R. Adriani, I. W. Mangku, and R. Budiarti, “ASYMPTOTIC DISTRIBUTIONS OF ESTIMATORS FOR THE MEAN AND THE VARIANCE OF A COMPOUND CYCLIC POISSON PROCESS”, BAREKENG: J. Math. & App., vol. 20, no. 1, pp. 0453-0464, Nov. 2025.
Issue
Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Section
Articles

Copyright (c) 2025 Ika Reskiana Adriani, I Wayan Mangku, Retno Budiarti

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