Strong Consistency and Asymptotic Distribution of Estimator for the Intensity Function Having Form of Periodic Function Multiplied by Power Function Trend of a Poisson Process

  • Nina Valentika
  • I. Wayan Mangku
  • Windiani Erliana
Keywords: Asymptotic Distribution, Intensity Function, Power Function Trend, Strong Consistency

Abstract

This manuscript discusses the strong consistency and the asymptotic distribution of an estimator for a periodic component of the intensity function having a form of periodic function multiplied by power function trend of a non-homogeneous Poisson process by using a uniform kernel function. It is assumed that the period of the periodic component of intensity function is known. An estimator for the periodic component using only a single realization of a Poisson process observed at a certain interval has been constructed. This estimator has been proved to be strongly consistent if the length of the observation interval indefinitely expands. Computer simulation also showed the asymptotic normality of this estimator.

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References

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Arkin, B. L. & Leemis, L. M. (2000). Nonparametric estimation of the cumulative intensity function for a nonhomogeneous poisson process from overlapping realizations. Management Science, 46(7), 989–998.

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Published
2018-04-30
How to Cite
Nina Valentika, I. Wayan Mangku, & Windiani Erliana. (2018). Strong Consistency and Asymptotic Distribution of Estimator for the Intensity Function Having Form of Periodic Function Multiplied by Power Function Trend of a Poisson Process. International Journal of Engineering and Management Research, 8(2), 232-236. Retrieved from https://www.ijemr.net/ojs/index.php/ojs/article/view/391
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Articles