International Journal of Mathematical, Engineering and Management Sciences

ISSN: 2455-7749

Parametric Bootstrap Methods for Estimating Model Parameters of Non-homogeneous Gamma Process

Yasuhiro Saito
Department of Maritime Safety Technology, Japan Coast Guard Academy, 5-1 Wakabacho, Kure, 737-8512, Japan.

Tadashi Dohi
Department of Information Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima, 739-8527, Japan.

DOI https://dx.doi.org/10.33889/IJMEMS.2018.3.2-013

Received on April 17, 2017
  ;
Accepted on September 27, 2017

Abstract

Non-Homogeneous Gamma Process (NHGP) is characterized by an arbitrary trend function and a gamma renewal distribution. In this paper, we estimate the confidence intervals of model parameters of NHGP via two parametric bootstrap methods: simulation-based approach and re-sampling-based approach. For each bootstrap method, we apply three methods to construct the confidence intervals. Through simulation experiments, we investigate each parametric bootstrapping and each construction method of confidence intervals in terms of the estimation accuracy. Finally, we find the best combination to estimate the model parameters in trend function and gamma renewal distribution in NHGP.

Keywords- Bootstrap, Non-homogeneous gamma process, Trend function, Confidence interval.

Citation

Saito, Y., & Dohi, T. (2018). Parametric Bootstrap Methods for Estimating Model Parameters of Non-homogeneous Gamma Process. International Journal of Mathematical, Engineering and Management Sciences, 3(2), 167-176. https://dx.doi.org/10.33889/IJMEMS.2018.3.2-013.

Conflict of Interest

Acknowledgements

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