Research Article Open Access

Kernel Type Estimator and Statistical Properties for Intensity Function of Periodic Poisson Process with Power Function Trend

Ro’fah Nur Rachmawati1
  • 1 Bina Nusantara University, Indonesia

Abstract

Problem statement: In this study, we construct the estimation for a periodic component of the intensity function of a periodic Poisson process in the presence of power function trend by using the general kernel function. Beside that we also construct the statistical properties of the estimator. Approach: It is considered the worst case where there is only available a single realization of the Poisson process having intensity which consist of a periodic component and a power function trend, observed in the interval [0, n]. It is assumed that the period of the periodic component and the slope of the power function trend are known. Results: It has been formulated the estimator and asymptotic approximations to the bias and variance of the estimator. Conclusion: The estimator that we construct is asymptotically unbiased estimator for a periodic component of the intensity function of a periodic Poisson process in the presence of a power function trend.

Journal of Mathematics and Statistics
Volume 8 No. 3, 2012, 403-412

DOI: https://doi.org/10.3844/jmssp.2012.403.412

Submitted On: 29 February 2012 Published On: 6 November 2012

How to Cite: Rachmawati, R. N. (2012). Kernel Type Estimator and Statistical Properties for Intensity Function of Periodic Poisson Process with Power Function Trend. Journal of Mathematics and Statistics, 8(3), 403-412. https://doi.org/10.3844/jmssp.2012.403.412

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Keywords

  • Unbiased estimator
  • intensity function
  • several nonparametric methods
  • asymptotic normality
  • statistical properties