Estimation of Change Point in Poisson Random Variables Using the Maximum Likelihood Method
American Journal of Theoretical and Applied Statistics
Volume 5, Issue 4, July 2016, Pages: 219-224
Received: May 27, 2016; Accepted: Jun. 18, 2016; Published: Jul. 11, 2016
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Authors
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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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.
Keywords
Change Point, Poisson Regression, Maximum Likelihood Estimation, Likelihood Ratio Test
To cite this article
Shalyne Nyambura, Simon Mundia, Anthony Waititu, Estimation of Change Point in Poisson Random Variables Using the Maximum Likelihood Method, American Journal of Theoretical and Applied Statistics. Vol. 5, No. 4, 2016, pp. 219-224. doi: 10.11648/j.ajtas.20160504.18
Copyright
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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