Estimation of Change Point in Poisson Random Variables Using the Maximum Likelihood Method

Shalyne Nyambura; Simon Mundia; Anthony Waititu

doi:doi:10.11648/j.ajtas.20160504.18

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Estimation of Change Point in Poisson Random Variables Using the Maximum Likelihood Method

Shalyne Nyambura, Simon Mundia, Anthony Waititu

Published in American Journal of Theoretical and Applied Statistics (Volume 5, Issue 4)

Received: 27 May 2016 Accepted: 18 June 2016 Published: 11 July 2016

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Abstract

The point at which a process undergoes a significant shift from its usual course is known as change point. Change point analysis entails testing for the presence of change in a given process, and the location of a single or multiple change points. This study presents a maximum likelihood estimate of a single change point in a sequence of independent and identically distributed Poisson random variables which are dependent on some covariates. A Poisson regression model is used to estimate the mean parameter and the likelihood function. A likelihood ratio test is conducted to check whether change exists with critical values of the test being obtained as in Gombay and Horvath [9]. The procedure is validated for simulated data for cases when there is no change and when there is a predefined change point with special application to incidence of road accidents in Kenya.

Published in	American Journal of Theoretical and Applied Statistics (Volume 5, Issue 4)
DOI	10.11648/j.ajtas.20160504.18
Page(s)	219-224
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Change Point, Poisson Regression, Maximum Likelihood Estimation, Likelihood Ratio Test

References

[1]	Amiri, A. and Allahyari, S. (2011), Change point estimation methods for control chart post-signal diagnostics: A literature review. Quality Reliable Engineering International, 28 (7): 673–685.
[2]	Boudjellaba, H., MacGibbon, B., and Sawyer, P. (2001), On exact inference for change in a Poisson sequence. Communications in Statistics - Theory and Methods, 30 (3): 407–434.
[3]	Carlin, B. P., Gelfand, A. E., and Smith, A. F. M. (1992), Hierarchical Bayesian analysis of change point problems, Applied Statistics, 41 (2): 389.
[4]	Chang, Y. P. (2001). Estimation of parameters for non homogeneous Poisson process: Software reliability with change-point model. Communications in Statistics-Simulation and Computation, 30 (3): 623–635.
[5]	Chen, J. and Gupta, A. K. (2012), Parametric Statistical Change Point Analysis, Birkhauser Boston.
[6]	Cooper, G. M. and Hausman, R. E. (2014), The cell: A molecular approach. The Quarterly Review of Biology, 89 (4): 399–399.
[7]	Cooper, J. A. (2004). Biomedical research, Academic Medicine, 79 (7): 710.
[8]	Farber, E. (1988), Cancer development and its natural history: A cancer prevention perspective. Cancer, 62 (S1): 1676–1679.
[9]	Gombay, E. and Horvath, L. (1996), On the rate of approximations for maximum likelihood tests in change-point models, Journal of Multivariate Analysis, 56 (1): 120–152
[10]	Mundia, S. and Waititu, A. (2014), The power of likelihood ratio test for a change-point in binomial distribution, Journal of Agriculture, Science And Technology, 16 (3).
[11]	Nelder, M. and Therneau (1993), Generalized linear models (2^nd ed.), Journal of the American Statistical Association, 88 (422): 698.
[12]	Syamsunder, A. and Naikan, V. (2008). Hierarchical segmented point process models with multiple change points for maintained systems. International Journal of Reliability, Quality And Safety Engineering, 15 (03), 261-304.

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APA Style

Shalyne Nyambura, Simon Mundia, Anthony Waititu. (2016). Estimation of Change Point in Poisson Random Variables Using the Maximum Likelihood Method. American Journal of Theoretical and Applied Statistics, 5(4), 219-224. https://doi.org/10.11648/j.ajtas.20160504.18

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ACS Style

Shalyne Nyambura; Simon Mundia; Anthony Waititu. Estimation of Change Point in Poisson Random Variables Using the Maximum Likelihood Method. Am. J. Theor. Appl. Stat. 2016, 5(4), 219-224. doi: 10.11648/j.ajtas.20160504.18

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AMA Style

Shalyne Nyambura, Simon Mundia, Anthony Waititu. Estimation of Change Point in Poisson Random Variables Using the Maximum Likelihood Method. Am J Theor Appl Stat. 2016;5(4):219-224. doi: 10.11648/j.ajtas.20160504.18

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@article{10.11648/j.ajtas.20160504.18,
  author = {Shalyne Nyambura and Simon Mundia and Anthony Waititu},
  title = {Estimation of Change Point in Poisson Random Variables Using the Maximum Likelihood Method},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {5},
  number = {4},
  pages = {219-224},
  doi = {10.11648/j.ajtas.20160504.18},
  url = {https://doi.org/10.11648/j.ajtas.20160504.18},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20160504.18},
  abstract = {The point at which a process undergoes a significant shift from its usual course is known as change point. Change point analysis entails testing for the presence of change in a given process, and the location of a single or multiple change points. This study presents a maximum likelihood estimate of a single change point in a sequence of independent and identically distributed Poisson random variables which are dependent on some covariates. A Poisson regression model is used to estimate the mean parameter and the likelihood function. A likelihood ratio test is conducted to check whether change exists with critical values of the test being obtained as in Gombay and Horvath [9]. The procedure is validated for simulated data for cases when there is no change and when there is a predefined change point with special application to incidence of road accidents in Kenya.},
 year = {2016}
}

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TY  - JOUR
T1  - Estimation of Change Point in Poisson Random Variables Using the Maximum Likelihood Method
AU  - Shalyne Nyambura
AU  - Simon Mundia
AU  - Anthony Waititu
Y1  - 2016/07/11
PY  - 2016
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DO  - 10.11648/j.ajtas.20160504.18
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 219
EP  - 224
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20160504.18
AB  - The point at which a process undergoes a significant shift from its usual course is known as change point. Change point analysis entails testing for the presence of change in a given process, and the location of a single or multiple change points. This study presents a maximum likelihood estimate of a single change point in a sequence of independent and identically distributed Poisson random variables which are dependent on some covariates. A Poisson regression model is used to estimate the mean parameter and the likelihood function. A likelihood ratio test is conducted to check whether change exists with critical values of the test being obtained as in Gombay and Horvath [9]. The procedure is validated for simulated data for cases when there is no change and when there is a predefined change point with special application to incidence of road accidents in Kenya.
VL  - 5
IS  - 4
ER  -

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Author Information

Shalyne Nyambura

Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Simon Mundia

Department of Statistics and Actuarial Sciences, Dedan Kimathi University of Technology, Nyeri, Kenya
Anthony Waititu

Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya

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APA Style

Shalyne Nyambura, Simon Mundia, Anthony Waititu. (2016). Estimation of Change Point in Poisson Random Variables Using the Maximum Likelihood Method. American Journal of Theoretical and Applied Statistics, 5(4), 219-224. https://doi.org/10.11648/j.ajtas.20160504.18

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ACS Style

Shalyne Nyambura; Simon Mundia; Anthony Waititu. Estimation of Change Point in Poisson Random Variables Using the Maximum Likelihood Method. Am. J. Theor. Appl. Stat. 2016, 5(4), 219-224. doi: 10.11648/j.ajtas.20160504.18

Copy | Download

AMA Style

Shalyne Nyambura, Simon Mundia, Anthony Waititu. Estimation of Change Point in Poisson Random Variables Using the Maximum Likelihood Method. Am J Theor Appl Stat. 2016;5(4):219-224. doi: 10.11648/j.ajtas.20160504.18

Copy | Download

@article{10.11648/j.ajtas.20160504.18,
  author = {Shalyne Nyambura and Simon Mundia and Anthony Waititu},
  title = {Estimation of Change Point in Poisson Random Variables Using the Maximum Likelihood Method},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {5},
  number = {4},
  pages = {219-224},
  doi = {10.11648/j.ajtas.20160504.18},
  url = {https://doi.org/10.11648/j.ajtas.20160504.18},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20160504.18},
  abstract = {The point at which a process undergoes a significant shift from its usual course is known as change point. Change point analysis entails testing for the presence of change in a given process, and the location of a single or multiple change points. This study presents a maximum likelihood estimate of a single change point in a sequence of independent and identically distributed Poisson random variables which are dependent on some covariates. A Poisson regression model is used to estimate the mean parameter and the likelihood function. A likelihood ratio test is conducted to check whether change exists with critical values of the test being obtained as in Gombay and Horvath [9]. The procedure is validated for simulated data for cases when there is no change and when there is a predefined change point with special application to incidence of road accidents in Kenya.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Estimation of Change Point in Poisson Random Variables Using the Maximum Likelihood Method
AU  - Shalyne Nyambura
AU  - Simon Mundia
AU  - Anthony Waititu
Y1  - 2016/07/11
PY  - 2016
N1  - https://doi.org/10.11648/j.ajtas.20160504.18
DO  - 10.11648/j.ajtas.20160504.18
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 219
EP  - 224
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20160504.18
AB  - The point at which a process undergoes a significant shift from its usual course is known as change point. Change point analysis entails testing for the presence of change in a given process, and the location of a single or multiple change points. This study presents a maximum likelihood estimate of a single change point in a sequence of independent and identically distributed Poisson random variables which are dependent on some covariates. A Poisson regression model is used to estimate the mean parameter and the likelihood function. A likelihood ratio test is conducted to check whether change exists with critical values of the test being obtained as in Gombay and Horvath [9]. The procedure is validated for simulated data for cases when there is no change and when there is a predefined change point with special application to incidence of road accidents in Kenya.
VL  - 5
IS  - 4
ER  -

Copy | Download